You seem to have figured most of it out yourself. A bit odd that you have exterior walls on both sides?
I have to admit I don't really know about the drain being imagined in the exterior wall. But I think it's okay.
If you're going to replace the drain upwards later, I wonder how that will work if you finish the bathroom first? You should install a jet coupling at the ceiling so you can access it from above.
I don't really get the feeling that you've had a company involved in this project that has approval from Säker Vatten.
It should be added that it's probably not dangerous at all to embed the water pipes the way it’s been done. If you just plaster and tile over the pipes, they won't freeze if you have a normal basement wall and have the heating on inside.
But rules are rules. If you want to do it right, you'll have to redo.