They do in fact offer all you can eat. I got it a few months back around 11:30 am.

Yes, they have two all-you-can-eat options (one is around $30 while the other one is around $35)

No

Yes, they have grill yourself or grill in kitchen

11:30a-9:30p every day indicated on their website, although some sources indicate open until 10p Fri/Sat. I'd call to confirm if your timing would require open until 10p those days.