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

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.