The purpose of the sign is to keep the liberal parents from whining about the safety of the children. Guns are dangerous and not having one around is the best option. Sarcasm intended here.
Potentially, but have you had it prosecuted down there? In my 15 years have not seen a gun trespass. But I don't know it all . . . just ask any ex-girlfriend.
Nope, but then again I don't know that I've ever seen a sign locally which references trespass or denial of entry.
I think in most counties there is little to no chance that you get prosecuted on something like that. Then again, if you are in Marion, Lake, Allen or a few others, all bets are off.