Oh no. It appears I'm developing a reputation of some kind. . .
The case that comes to mind is Tinker v. Des Moines, 393 U.S. 503. The wearing of anti-war armbands by public school students was considered akin to "pure speach." That case discusses the "context" issues you brought up, such as time, place, etc.
My understanding is that, if an action is labeled "conduct," it is afforded no First Amendment protection at all (aside form assembly or religious conduct). So, no statute could be facially unconstitutional solely for banning a certain type of conduct, unless it infringed on a liberty interest or implicated equal protection issues. So, the answer to 3(a) is that a challenge to a statute that banned face painting except among certain groups is that it could be struck down on equal protection grounds if the painting was considered conduct and not speech. But, if the painting is considered speech (as it is likely to be), there are at least two ways to challenge the statute-- equal protection and First Amendment grounds.
I'm not sure I understand what you're getting at in number 3. If face painting is determined to be conduct, and not speech, then you are left with equal protection arguments, and those are almost always losers unless race or ethnicity are implicated.
But, personally, I think such a statute would be a violation of a non-football-game-attending person's right to liberty. I would lose that one every time too.