If I say that someone was mean to me, does that imply that they were conscious of it?

Mean does not necessarily entail intent.

A person may be mean in several senses. To start with, I looked at the definition and examples in the Oxford English Dictionary. "Mean, adj.1," definition 5d is closest to the definition you cite, since it includes "unkind":

d. colloquial (originally U.S.). Of a person, a person's actions, etc.: disobliging, uncooperative; unpleasant, unkind; vicious, cruel.

1841 ‘Dow, Jr.’ Short Patent Serm. 78 [One girl] thought me real mean for uttering such super-diabolical sentiments.

[...]

1891 R. T. Cooke Huckleberries 14 It would be awful mean of me to leave you here alone.

I selected these two examples, the first being the earliest example, because in them mean labels someone's personal qualities but not necessarily their intent. In the 1841 example, someone thinks the speaker is "real mean" because they say bad things. I don't see a fair way to distinguish attributing a quality (like being unpleasant) and attributing intent (like cruel) in this example. The person is mean for a specific action, and it is not clear whether that ascription implies intent.

The second example uses mean (with awful in a regional sense meaning something like "very") to describe the disposition of the speaker in a hypothetical situation. I find it odd to describe intent hypothetically. I'd expect the focus to be on wishing to do something, e.g. "to want to leave you here alone." Instead, mean here feels like a quality or characteristic tied to the act itself: "to leave you here alone." Someone who leaves someone else here alone is awful mean no matter the intent, just like someone who holds the door open for me would be awful kind no matter the intent.

Based on those two examples, mean pertains to actions and characteristics of a person that need not be connected to intent.

First, let's consider the etymology of the word mean, and the various ways it has been used historically:

Mean (v.1): [For example, "What do you mean?"]

• "intend, have in mind;" Middle English mēnen, from Old English mænan "intend (to do something), plan; indicate (a certain object) or convey (a certain sense) when using a word," from Proto-West Germanic *menjojanan (source also of Old Frisian mena "to signify," Old Saxon menian "to intend, signify, make known," Dutch menen, German meinen "think, suppose, be of the opinion"), from PIE *meino- "opinion, intent" (source also of Old Church Slavonic meniti "to think, have an opinion," Old Irish mian "wish, desire," Welsh mwyn "enjoyment"), perhaps from root *men- (1) "to think."
• From late 14c. as "have intentions of a specified kind" (as in to mean well). Of a person or thing, "to be of some account, to matter (to)," by 1888. Conversational question you know what I mean? attested by 1834.

Mean (adj.1)

• c. 1200, mēne, "shared by all, common, general," a sense now obsolete, shortened from imene, from Old English gemæne "common, public, general, universal, shared by all," from Proto-Germanic *ga-mainiz "possessed jointly" (source also of Old Frisian mene, Old Saxon gimeni, Middle Low German gemeine, Middle Dutch gemene, Dutch gemeen, German gemein, Gothic gamains "common"), from PIE *ko-moin-i- "held in common," a compound adjective formed from collective prefix *ko- "together" (Proto-Germanic *ga-) + *moi-n-, suffixed form of PIE root *mei- (1) "to change; exchange." Compare second element in common (adj.), a word with a sense evolution parallel to that of this word.
• Meaning "of common or low origin, inferior in rank or status" (of persons) is attested from early 14c. Sense of "ordinary, inferior in attainment or skill" is from late 14c. Also from late 14c. as "poor in quality, of little value," though this sense survived longer in American than in England. James Stirling, in "Letters from the Slave States" [London, 1857], mentioning mean whites (poor whites in the South who do manual labor and are looked down on by the slaves) notes, " 'Mean' is an Americanism for 'poor,' 'shabby.' They speak here of a 'mean' hotel, a 'mean' dinner, &c."
• The pejorative sense of "without dignity of mind, destitute of honor, low-minded" is from 1660s; the specific sense of "stingy, niggardly" is recorded by 1755; the weaker sense of "disobliging, pettily offensive" is from 1839, originally American English slang. All these developments of the English word were furthered by its coincidence in form with mean (adj.2) "middle, middling," which also was used in disparaging senses, and OED notes that some usages of mean it cites "might be referred almost equally to the native and to the foreign adj.; the truth is probably that they are of mixed ancestry."
• The inverted [or litotic] sense of "remarkably good" (as in plays a mean Rhythm Master) first recorded c. 1900, perhaps from phrase "no mean _______ (e.g., ability), meaning "not inferior" (1590s, also, "not average," reflecting further confusion with mean (adj.2.)). [Example, "He was a brilliant athlete of no mean ability."]

Mean (n.)

• "that point, place, or state which is halfway between extremes;" c. 1300, originally in music, "a tone intermediate between two other tones," from Old French meien "middle, means, intermediary," noun use of adjective from Late Latin medianus "of or that is in the middle," from Latin medius "in the middle," from PIE root *medhyo- "middle."
• The modern range of senses in English mostly appeared late 14c.: "course of action; method, way of attaining an end" (as in ways and means;by means of; by all means; by no means); also "the golden mean, moderation;" and "something physically between two extremes." The mathematical sense, "a quantity having a value intermediate between the values of other quantities, the average obtained by adding several quantities together and dividing the sum by their number" is from mid-15c. Some senses reflect confusion with mean (adj.1).

Mean (v.2)

• "calculate an arithmetical mean," 1882, from mean (n.).

Mean (adj.2)

• "occupying a middle or intermediate place;" mid-14c., of persons, "of middle rank" (but this is possibly from, or mixed with, mean (adj.1)); from Anglo-French meines (plural), Old French meien, variant of moiien "mid-, medium, common, middle-class" (12c., Modern French moyen), from Late Latin medianus "of the middle," from Latin medius "in the middle" (from PIE root *medhyo- "middle").
• From late 14c. as "in a middle state, between two extremes." Meaning "intermediate in time, coming between two events or points in time" is from mid-15c. (the sense in meanwhile, meantime). The mathematical sense "intermediate in a number of greater or lesser values, quantities, or amounts" is from late 14c.

In answer to your questions:

• Can I be mean to a person I don't know exists?

I'm not sure what you are getting at here.

• Can I be mean to someone who I am affecting indirectly?

I'm not sure what you are getting at here.

• Is intent a requisite in being mean to someone?

I cannot imagine a person being mean who does not intend to be mean, unless, of course, the target of his meanness interprets incorrectly the remark or the behavior negatively and pejoratively. For example: [The thought-to-be-mean person:] "Your performance was not half bad!" [The person who misconstrues the remark as being mean]: "Hmmm, he thinks I didn't perform well. How mean!"

• If someone didn't intend to hurt someone, is it fair to say that they were mean?

No, just misunderstood. That happens all the time, especially with people who tend to be ultra-sensitive and quick to take offense.

Mean, as you've used it, implies intent.

I'm going to go with Websters here:

Entry 2/4 (5)(b) mean: characterized by petty selfishness or malice. (Websters)

If we're talking about "the mean man", then we're invoking the "selfishness" portion of the definition. A mean man doesn't necessarily direct his meanness to a particular individual and, in that sense, may have unintentionally affected another negatively without the specific intent to do so.

But, the way you're using it, "The man was mean to me", suggests a focus and intentionality by "the man" (or "someone" in your example) and invokes the "malice" portion of the definition. Malice, if nothing else, is a word of intention (Websters)

1. You can't be mean to someone who you don't know exists. But, you could have a mean disposition that unintentionally affects those around you.
2. You can be mean to someone by doing things that indirectly affect them, provided that's what you intend.
3. I think I've answered that –Yes.
4. If A didn't intend to hurt B, it might be fair to say that A was a mean person, but not that A was mean to B.