1. Beach Club Marketplace has stuff, yes, but it's Disney pricey. That said, I would often buy the cheese plate from there at the end of an evening for some ridiculous price.
2. Depends on where you are, but it's close. We've been under 5 minutes from our room door to the gates before.
3. Never taken a bus, only the boat and walked. 15-20 minutes with the stop(s) it has to make en route - Swan & Dolphin at least, possibly Boardwalk too - I can't recall the order. Coming home, walking is often quicker due to the line for the boat.
4. You won't get into Beaches & Cream without an
ADR or a long wait. Around the lake, ESPN Club and Big River Grille are reasonable options. However, if you can spare the entry on your ticket, I'd be tempted to wander into Epcot, get some chips from the Yorkshire County Fish Shop, a beer and sit and watch the British Revolution.