Question(s) Regarding the Okina Movie Theater

I have three questions about how the movie theater mechanic works.

1. Do the stat bonuses that you gain from on a party member carry over to NG+?

2. Is there a limit to how many stat bonuses you can get on a party member? (Can you max out stats, and if not, what is the limit?)

3. Does going on days when you’re invited by a party member to go grant extra bonuses?