You can definitely park at BW, Yacht, or Beach for your ADR. In compliance with Disney’s rules and as a courtesy to guests of the resort, you’re supposed to move your car after eating, so that guests can park at the resort they’re sleeping at. But in reality, it’s unlikely that you’ll have any problem leaving the car there (which I can attest to after many times watching the exodus of cars from the BW parking lot after Epcot closes). As an alternative, you could make a reservation to eat at one of the Swan/Dolphin restaurants. They have a flat-rate charge for parking, but most if not all of the table service restaurants (il Mulino I know for sure) will comp it.
No problem with that at all. The IG is open for anyone with a valid ticket for the event (and is the normal entrance for guests at the Epcot resorts).
You mean parking at the main Epcot entrance? Oh my, I might think about Garden Grill (character meal), but you really need to ask that question on the Restaurants forum!