Are they requiring proof of vaccination to get into games?

Proof of vaccination as well as masks.

Doesnt hurt to be prepared so go ahead and have your vaccination card available along

Yes they are

Yes. Have your vax card and a mask.

Yes, at least at the events we have gone to. Pro tip, don't wait to bring it up on your phone for vaccines or tickets, have it ready, too many people holding up the lines ( even for parking) and suddenly they have a phone problem. We showed our physical Vaccine cards but tickets are paperless. Same as no cash allowed inside which sucks, but I understand, but still hate the "cashless society" thing.

Yes

I'm not sure on this.. I suggest calling ticket sellers and asking

Absolutely yes, come with your vaccine card or proof or you're not getting in.

I'm guessing yes. We had to show proof of vaccination to get into the concert, it you have to have a negative test up to 72 hours in advance