Can I raise the listed rent on a rental property due to high demand?

Not a lawyer but this seems like a very bad plan.

What you're hoping to do here looks very much like a classic bait-and-switch scam. Advertising a low price to attract customers and then declining to offer the goods at that price is generally not allowed and could cause you significant liability. You'd need to look at Philadelphia's landlord-tenant laws and consumer protection laws to determine what liability you'd face and/or whether you fall under one of the law's exceptions. But it looks to this non-lawyer like you'd be pretty squarely covered.

Small time landlord here.

I would say don't count your chickens before they hatch. "expressing an interest" is not the same thing as putting down a security deposit and signing a lease. I've had many people "express interest" who then ghost me. Finding an apartment is a lot like dating. These potential tenants might also have expressed interest in two or three other places. until you have a check in your hand you really don't know. I'd suggest stick with your original price and see what happens. If you do get it signed quickly, you can raise the rent the next time around.

If you haven't collected money from applicants or made any agreements with them, then they aren't harmed by you changing rent, in a legally actionable way at least. As comments point out, some people might view their wasted time as an incredible offense and seek to harm you. If you have collected application fees then you either shouldn't raise the rent or you should refund all application fees if the applicants are not interested at the higher price. Legally I don't see a problem assuming no harm is done to the applicants, but go ask a lawyer in your region to confirm.

Whether or not you should depends primarily on how much below market you actually went. If you listed 20% below market value, then people wouldn't be shocked if you indicated it was a listing mistake. If it's 5% under market value, you come across as someone who is trying to squeeze as much out as you can. Some grey between those ranges, but don't expect current applicants to stick around at a higher rate.

I consistently rent on the low-end of market value because I want a wide tenant-pool to choose from. High quality tenants that feel they are getting a good value are worth a lot more than getting the highest possible rent. You want a fair rent that you're comfortable not raising too significantly if your tenants are interested in renewing. That's my model at least, I'm happy to sacrifice some rent to keep turnover low and maintain high quality tenants.

Yes you can. Just tell them that there was a lot of interest and someone offered 9 % more than the advertised price and "if you offer +10 % you are first in the line".

It is common understanding between civilized, honorable people that a promise is a promise. When you accept an application you make a promise. Namely, that unless the prospective tenant happens to meet certain defined disqualifying criteria, they will be given the right to sign on the exact terms discussed.

The person who submitted an application for a lower rent may not want to apply at the higher rent, so if you raise your asking rent without giving them a chance to sign at the original amount, you are wasting the time which they spent on your application. You have also made them submit confidential personal information on a false premise (that they would thereby gain the opportunity to sign a lease at the lower price). You could get in trouble here if the authorities decide for instance that you have no intention of renting at all, and are merely running a scam to collect personal information.

Typically an application also includes an application fee. This is another problem, as if the application is going to be thrown out that money is essentially being cheated out of the applicant. A particularly angry applicant (which they have every right to be given that this sort of sell-side price hiking is considered extremely rude and improper) may decide to sue you in small claims court for the fee. That will open the door to being sued for legal damages, time lost, and the local government further deciding to review your practices. Keep in mind that politically speaking, punishing shady landlord practices will likely be a popular move these days.

I would say that if you really want to raise your rent, you should at least refund the application fee to the applicants and apologize. You should also destroy the information they submitted and make this clear. There's nothing you can do about the wasted time, but hopefully none of the applicant will bother trying to get at you for just that. Also, carefully review the language in your application and your local laws, because it is conceivable that there may be local laws that require you to honor all applications received.

I'd say 20 interested parties is good, that allows you to look at non-monetary factors as well -- do they leave an impression on you as if they will take good care of things, do they seem like people who'd get along with the neighbours, so if someone goes on holiday, they will watch each others' houses to prevent burglaries.

You are still competing with other landlords for good tenants. A handyman might not want to pay as much as a hipster running a venture capital funded startup, but they will also complain a lot less about minor issues that are technically your responsibility but can be fixed in five minutes.

I would very strongly recommend against doing so, especially during this pandemic, when evicting people for non-payment will be impossible for a long time. Rather, if you have a lot of prospective tenants to pick from, research them (Facebook, LinkedIn, etc) ask them for a credit report(or at least a Credit Karma screenshot) and choose the one that seems like a sure bet for not defaulting, i.e. they still have something to lose, like very good credit, or they have a job that is extremely unlikely to be cut, or they at least seem like a responsible, organized person. It's much better to have 10% less with a high level of confidence, because a good tenant is getting a great deal, than risk 100% less + risk of damage to the apartment. If no-one fits the bill, accept the temporary loss and keep looking, with maybe another 5% cut to stimulate interest.

One option is to go ahead and increase the advertised rate on Zillow for any new contacts, but also send everyone who has already contacted you a message telling them that you will still honor the previously advertised price for them. Even so, many of those people could view this as a type of high-pressure sales tactic and run from that.