1. Is there a limit for trashing cards per turn? You have 3 moves but can they all be trashing a card and drawing a new one?
The limit is simply the number of actions you have per turn. If you want you can use all your actions to trash cards, but I wouldn't trash them all at once since the first or second card you draw could give you the action you're looking for.
2. Did somebody try to play the base game with the move rule from the expansion (you can discard one card in order to move to an adjacent transformer)? Would this make the game easier?
You can use that rule in the main game as well. It does make it slightly easier but on the other hand it also speeds up the game, which is a plus in my book! I don't feel it becomes unbalanced since every player can benefit from it.