Through monsters is fine. Through doors/walls is not, as closed doors prevent counting of spaces. Black walls are completely impassible by any means.
No, they cannot. It needs to be within 3 spaces, but closed doors and walls prevent the spaces from being adjacent.
Well, it seems that it's time to reread the rulebook. Again.
So, in this case
Yeah, I got that.
All you need is to be within 3 spaces. But when you count your distance on the field it won't be necessarily a straight line and, like in my example above, you can go round the wall, yes?