No, a sequel would fit perfectly, because at the end the game is rebooting. You can give all characters the knowledge about the first part. So the title “Thimbleweed Park Rebooted” would fit perfectly. 
No, there could be an update to the “game”. So you can introduce new locations, characters and everything you like.
btw: Another possibility would be that Chuck was wrong.
Or a text adventure… (see our discussion here: Pre-release Fanart - C64 Text Adventure)
Yep, same here. But I’m not a fan of sequels either.