What do I need to consider for a justice system for powered people by powered people?

Treat Super Powers Like Gun Ownership

The US legal system already pretty much addresses this problem in the form of "aggravated" and "reckless endangerment" crimes.

To dissuade the use of deadly weapons, the sentencing for any crime becomes more severe anywhere a weapon is involved in the execution of the crime, even if it is not used to harm anyone. If you rob a store with your bare hands, it is robbery, but if you use a gun to do it, it is aggravated robbery. Using super powers to rob a store creates the same sort of unfair, traumatizing, and increasingly dangerous sort of power dynamic as a gun; so, when a super does use thier powers in a crime, the punishment is elevated which would hopefully be enough to convince at least some would be criminal supers to commit crimes using thier mundane abilities as much as possible.

On the same token, carrying a gun is not illegal, getting into a fight with a gun on your person is not an aggravated crime, shooting a gun in a safe environment not illegal, and being a super is not illegal. Supers are allowed have powers and use them in ways that common sense would tell you are safe and legal, but using your powers recklessly (like firing a gun blindly into the air) is a crime unto itself. This leaves the subject of using one's powers somewhere along the vein of, if you are not sure it is safe, you can get in trouble for it.

There may also be certain zero tolerance zones, like gun free zones, where using powers is entirely forbidden.

The advantage of treating all powers like gun ownership is that you don't criminalize anyone for having one power or another, you only criminalize its misuse. Using mind control to steal a car is still grand theft auto, but now it is aggravated grand theft auto. Using super strength to crush a person's skull is still murder, but now it's aggravated murder. Creating a situation that blinds drivers is reckless endangerment whether you do it by throwing eggs at thier windshields or by conjuring up a smoke screen. The definition of crimes are all about what you are doing instead of what powers you are using to do it; so, you can keep your code of laws relatively fair and simple.

As a bonus, this approach to super power law would be pretty consistent with normal people law such that it would work even outside of thier own special culture.

Side note: in some countries, people with unordinary physical abilities like formal martial arts training can be prosecuted for aggravated assault even without a weapon. In a since, these jurisdictions already handle "super powers" this way.

Addressing your specific concerns

Moral implications: Legal systems are about ethics, not morality. The general rule of law is that that which is not illegal is legal until it is not, and any moral implications beyond that is not for the courts to decide. Transferring the mind of a person with a terminal illness into the body of another that is otherwise brain-dead is perfectly legal as long as you can prove you are not killing either person in the process under the current definitions of murder. If it does kill one of the people, then you would need to petition legislatures to define this action as an exception to the law. If it's not illegal, but congress sees it as a "form of murder" then it could be made illegal.

Also, most US states also use precedent in the evaluation of the law to stand in for congressional decisions until the law can be refined. So, the first time someone decides to press charges for something ambiguous like this, it could be decided very quickly if it is considered murder or not by the first court case that evaluates it. Then everyone knows if that strange thing is or is not murder moving forward.

Excessive Damage to Property: Damage to property laws should suffice. The plaintiff brings you to court, damages are assessed, and you are required to pay restitution, and if the damages exceed a certain amount or your ability to repay them, then there can be felony charges that stack which could result in jail time.

Conduct of those with potentially intrusive abilities: Laws concerning fraud and coercion are generally left intentionally vague because people are so creative when it comes to finding new ways to do them. Fraud is defined as any intentional deception or misrepresentation used to benefit yourself or someone else, and coercion covers any use of threats, commands, and any use of force. So, if you can implant false memories or impulses directly into someone's mind, that is clearly Fraud. If you tell a person to jump off a bridge and they do, that is coercion. So, without modifying the law at all, most of the more insidious intrusive abilities are already covered.

As for simple mind reading, there are no laws to prevent it, but there are many laws to prevent the use of said knowledge. You can steal someone's PPI sure, but using it to take thier money is theft, using it to get into thier digital accounts is hacking, and using it create accounts in thier names is identity theft, using it to ruin a person's reputation is defamation, using it to manipulate them is blackmail, so on and so forth.

If you really want to crack down on psychic intrusion, you could expand CFAA law to cover the misuse of psychic abilities according to the same criteria that we evaluate hacking, since psychic intrusion and hacking are so similar in nature.

One thing you should consider is the possibility of super powers adjusting an individual's personality, and at the extreme, power-induced-psychosis or sapient/sentient powers. Let me outline a couple example cases:

• An individual develops some sort of changer-power which lets them transform into a bear or whatever. Unfortunately, when they're in bear-form, they can't keep "control" and often act far more violently than they would in human form. Even worse, the longer the individual goes without transforming, the more the "urge" to transform grows. Now, say this individual kills someone while in bear form. Are they at fault? Can they plead mental illness?

• An individual develops some sort of mover/shaker power which enables them to warp space into pocket dimensions and teleport. Unfortunately, with this power comes an extreme case of kleptomania. The individual gets physically ill if they do not regularly steal things to appease their power, and this can't be "cheesed": the individual needs to actually believe that they've stolen something to appease the power. How do you deal with this? What if it can be conclusively proven that the individual's kleptomania disappears inside a power-nullification zone?

• An individual develops an exotic "demon summoning" power and gains the ability to summon temporary "demons" which they can use to fight or whatever. Unfortunately, as a byproduct of his power, infernal creatures whisper in their head all the time and drive them to commit crimes or other nefarious deeds. Is the individual at fault? Can the demons be prosecuted in a court?

• An individual develops an extreme changer power which essentially transforms them into a ghost. While in ghost form, they can't interact with the world, eat, sleep, or even breathe. The only way to survive is if they're actively possessing someone--otherwise they suffocate if they can't hold their breath. Unfortunately, possession is very invasive and the ghost-individual instantly has full control of the victim along with instantaneous access to all their knowledge. How would a court handle something like this? Prohibiting the individual from possessing people would kill them, but at the same time, it would be very hard to fight a willing possessee without hopping through a couple unwilling bodies beforehand. Similar problems rise up with people who develop vampire-esque powers requiring them to drink blood, eat dreams, or be a cannibal to survive.

Build up from Tyranny

There are superhumans among us now. A tiny number of people, on paper, own (directly or indirectly) most everything. These could split into empires and armies clashing, suppressing, and ruling by force. Much like an overpowered superhero might.

But they don't. Why? These super humans are satisfied that concerns of great urgency to them are infrequent and can be worked out through a system. They are satisfied with roles as influencers, trend setters, deal makers, and moon shot-ers. They are satisfied that, at the moment, the benefits of arming and going to war with the world do not justify the expense to stability, mobility, safety, and peace of mind.

Similarly, your superhuman justice system would need to satisfy the people with the greatest strength that their needs can be cared for by that justice system. It means that sometimes justice might not be served, or sometimes their will be crisis between principles and the wants of one of these most mighty superhumans. But, as long as they are satisfied that what they care about is being taken care of expeditiously, it might be possible to convince them to hang up the cape and play chess, or make films, or something like that.

Build up also from Anarchy

The public consists of very large numbers. To provide for their needs is impossible, hence the adage "you can't please all of the people all of the time".

However, a public of normal or superhumans can be satisfied with a justice system that lets them know what to expect. In this case, the decisions made should (most of the time) be easily predictable by experts on the topic. It should be easy enough that the public can deal with a lot of justice requests on their own.

Examples: a written legal code (like the Lextalionis) with descriptions of requirements and penalties for non-compliance, a well-understood system of arbitrating disputes : who makes the decisions, how disputes are presented, timeliness; a written constitution that in broad strokes outlines principles of government; a mechanism for evolving the rules and procedures (a law- or rule- making body).

The public needs to trust that most of the time, "the process" delivers results they will be happy with. If they can rest assured the system will take care of them, the public will defend it.

Some Suggestions

Define person : everyone struggles with this one. From the ${3 over 5}^{ths}$ compromise in the constitution, to tribalism, to the elderly, to criminals, the insane, the young, the very young, those on life-saving equipment, and those without "gifts". Who is entitled to full protection of "the system"? Who gets less than full protection? Who gets nothing?

Themis.

There is a super whose power is to be the justice system. She is extremely old but not aged in appearance. She may be immortal. She has a depth of understanding beyond that of normal people and supers both and her gift is the gift of fairness. And she is blind.

Judicial matters involving supers (and sometimes those not) are brought before Justice.

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A problem with this system is that it has all the proverbial eggs in one basket. What if Justice were not able to carry out her duties? What if she were kidnapped and held for ransom? And how would this entity Justice comport herself in such a situation?

No one super who is drastically more powerful than anyone else

The way human society tends to "work" is that people are mostly safe because physically humans beings are more or less equal within a margin of error. Yes, some people are stronger than others, but in a straight-up fight stripped of followers and political power even the most brutal warlord is still human. Even the strongest person will still likely lose against a gang formed by the second, third, and fourth strongest. Even if you bring up differences in strength between men and women, those differences are in the sense of "on average". Women can still kill men if they have the element of surprise, have weapons, are more skilled fighters, are just bigger, etc.

What this means is that every individual in society has to be on their best behavior, because if they aren't the rest of society will gang up on them and take them down if they start negatively impacting the group. Introduce superpowers, however, and now you have a system where one person (like some super-psychic or flying brick) can set themselves up as leader through brute force and nobody can do anything about it. Reminds me of the saying in Greek myth where Zeus tells the other Olympians "I'm in charge because I'm the strongest, even if the rest of you all teamed up on me at once you could not bring me down" [paraphrased].

Human legal systems are mostly based on the concept of isonomy "all individuals are essentially equal [by which I mean talents like intellect or physical stature are negligable], and therefore shall be treated as equal under the law". Except now you have a situtation where this is blatantly not true. Not only do you have a situation where people are not equal under the law (normals versus supers), but you have individuals that even if you wanted to you cannot force to comply. Who is going to successfully arrest Superman if he breaks the law? So with that, you devolve into a society of barbarism with just one rule: don't make the super-gods mad. Society becomes intrisically based around what you and what you can do rather than who you are when you introduce variable superpowers (and people without) into the mix.

Incidentally, this is a lot of the reason why Superman makes a lot of people antsy despite being a big blue boyscout (which we'll hereafter call the "Lex Luthor argument"). Superman technically doesn't need humanity in any direct way. He doesn't rely on other people for food, or shelter, or resources. When he needs to pay taxes on the Fortress of Solitude he just crushes coal into diamonds. An army of normals couldn't stop him. An army of superheroes debatably couldn't stop him, unless you were very careful who you picked (i.e., other flying bricks) or very sneaky (read: Kryptonite). Humanity has no way to put a check on his power. There is nothing to stop him from setting himself up as a god-king through physical force beyond his own conscience. And most human beings aren't as virtuous as Superman (and there's the whole, "Clark Kent likes being normal" aspect, but that's neither here nor there).