Hey! Sorry for taking so long to answer!
1) Yes! The characters cannot move diagonally.
2) That's a good question. I made the rules with a solo gaming in mind, when a room is revealed you had to use your player's action, so the enemies will be revealed right away. But in a multiplayer game, you will wait the other players for that. I didn't thought in that, but it would be better to reveal the enemies right after revealing the room, so the other players can interact with them if they still have moves.
3) Yes, I made the figures with the colored base at the same size of the tile, so you can fold them to support the figures standed.