Retrofit bathtub or shower?

If the pipes from the basement work, then that is no problem at all. Only the shower tray should have the drain on the outer wall. I just can't imagine yet how you want to turn the wardrobe into a bathroom. I have no idea what the wardrobe looks like.

Exterior wall? Why? How the room looks doesn't matter. There is space. You can make everything look nice. I'll now have two installers come to clarify the technical aspects as well as the cost and effort.

Because in my opinion there are fewer conflicts with the underfloor heating there and the other pipes from the WC are also there. Everything can be done, but you should describe more precisely what you actually want. The wardrobe in your plan doesn't even have a door.

The pipes from the WC are in the separate room. Without underfloor heating, I wouldn't even ask the question in the forum. Then it wouldn't be a problem at all. I had hoped that someone had already retrofitted something similar regarding "pulling over" pipes or making a drain connection. Now the plumber I trust is coming to take a look and see what he thinks.