1. Lots to see. What are you most interested in? There is American history, museums, and beautiful outdoorsy stuff nearby. My brother lives in Cambridge and I visit him pretty often. During a 36 hr trip I did once, we actually just rented a car and drove up the coast to Maine. Ate some great local lobster, checked out some lighthouses, and saw some great beaches. If you are more into the city/historical stuff, do the freedom trail and just walk the downtown. Boston is super small and Uber has great availability. Do Boston common, ride the swan boat, check out the waterfront, etc. Boston is one of the best US cities to just spend a day exploring. Nothing is too omnipotent that you *can't* miss, its small, and the atmosphere is just as good as anything else. If you are a big history buff, get a car and see Walden pond and Lexington/Concord, etc.
2. Not too big into sweets. Maybe Boston Cream Pie from the Omni House? It was first done there.
3. Harpoon Brewery. Tours too.
4. No ideas here.
Have fun!