Feel free to sit anywhere, no matter what you're ordering. Depending on what time you go, though, it might be easier to sit in Sidelines -- there are cocktail tables and booths there, not just the bar. Sometimes the wait for SportsCentral can be loooong. The entire restaurant is also non-smoking now, including the bar area.
The video game area is in the store, it's not visible from the restaurant or bar. If you sit in a booth, though, there are individual TVs in there with video games and you can ask your server for the controllers. They don't always give them out during peak times, though, because the controllers can be hard to keep track of. During the day, though, you won't have a problem.
Yes, you do get a team discount in the store next door. It's whatever your discount percentage is. (So if you get the holiday stuff, even better!)