Updated: Terrain and items disappearing... in progress on terrain issue...

So, given that outdoor rooms is a category probably intended for outdoor placement only, rooms in the category deliberately place without a ceiling/roof.  They do this above ground too, and they also do it on the 2nd level basement (but the game puts a dirt covering above them).  You can still put the terrain back in place above the first basement level by clicking on a wall of the room and then on the yellow outline around it at the top:

 

Choose Build Ceiling, and it will redraw the terrain.  I think it also makes sense that objects are deleted above the room when you place it because they no longer have a floor or base to rest upon, and also, in some cases, I think objects from the basement level are then conflicting with objects at ground level.  Solution there would be to place your basement room first, redraw the terrain above it, and then place additional rooms/objects above.

 

Finally, you can delete a room in a basement by clicking on one of the walls to select it and then simply hitting your DEL key - it will delete the entire room.

 

Hope this info helps!