What size drain does the new shower need? Current codes require 2", and that may be 2" (although they sell 1.5" but it doesn't meet code - don't ask me why).
You don't want a horizontal trap arm under the shower - you want the trap under the new shower's drain. This may mean tearing up more of the floor. If it isn't too far to the main drain, you can probably replace that arm with a 2" and make everyone happy. Safer to replace an old trap if it is metal under there - pvc would be fine. Code requires the pipe be 2" underground minimum, so you may find that the pipe is 2", and you wouldn't have to tear out too much, maybe only the (possibly) 1.5" trap and riser...it probably bumps up to 2" on the outlet.
The shower pan works best and lasts longest if it is fully supported underneath. There are various things that work - stucolite, deck mud (sand and portland cement mix...heavy on the sand 4-6:1), and other stuff as well.