Shepard wouldn't be the first war hero in humanity's history, and generally speaking we don't dedicate museums to war heroes. Does Rome have a museum dedicated to Horatius Cocles, for example?
A statue in a city square maybe, but a museum seems a bit much.
No, but he (or she) would be the first human - or any other being - to save the entire galaxy, not to mention stop the reaper cycles tht had been going on for millions of years. I hardly think it is unreasonable to have a Shepard museum. At the very least they should have a major Shepard memorial out the front of a Reaper museum.
No.
I want Shepard to be forgotten. Disappeared into obscurity and never mentioned in-game.
Forgetting Shepard in the next game would be like Bioware biting its own hand off. There should be references where appropriate. I don't want him to have any involvement in the next game but You can't just ignore his contribution to the MEU. There are references to the First Contact War, the Rachni War and the Krogan Rebellions all throughout the trilogy so it makes sense to reference the Reaper War and, by association, Shep.