I have a season pass from six flags great adventure, if I bring my official souvenir cup, can I use that and the dining plan that is on my pass at your park?

Yes you can. Since it's owned by six flags your season pass and dinning pass will work at ALL six flags parks. Including your cup.

Yes. But using the bring a guest free option on your membership is a bit of hassle because you have to go to guest services first. Otherwise everything is same as home park

Yes

Yes season passes work at all locations