The hope is to make is so when you rotate dimensions, the map looks a bit like the world is turning to represent this. Not quite there yet, but my hope is that helps get an idea of what's going on.
This gets very painful mentally when you go above 3 dimensions though, I get a feeling many will need to give up trying to understand the whole maze in that situation and focus on only a few small views of it.
This is the point of this game really, to show you how your brain thinks about spaces, and how much harder it is to think about higher dimensions and how quickly we get lost in them.
As for a victory condition: There is currently no marker for when you get to the end, if you get to the point where you're in the top corner of the maze in every dimension then you're at where the end will eventually be.
I tried to rotate the view so the camera was suggesting up, I totally get how that can be confusing though. I'll need to think about how to make that easier for people in the future. Thank you for bringing this up!