I just left Hoi An today (Mar. 12th)! It's a very nice town. I cannot answer all your questions because I stayed in the town of Hoi An however I just wanted to offer what I know.

Question 2) From our hotel to the beach was 4km. You can pretty much rent a bike anywhere so there's no worries there.

Question 6) Right after Tet things can be hit or miss. I found some places don't open until 4 days after the holidays when others open 5 or 6 afterwards. Restaurants may be open but even if they are they may have a limited menu. I stayed in Hanoi during this time and in the touristy area there was a premium paid on menu items. Once that week past it was back to normal!