1. Monsters always take the most direct route to their target, even if there is terrain in the way. So they must move through it. Unless it's one of the very few pieces that even monsters can't go through.
2. Range isn't calculated that way. Range 2 doesn't mean there are two spaces between the attacker and target. It means one space, the target is on the second space. Terrain works the same way.
Thanks for confirming. I actually meant former, rather than latter, so I've edited accordingly. Didn't make sense otherwise. I was just uncertain because some terrain *does* seem to specify a certain number of spaces between, rather than "X spaces away from."