I'm looking at redoing my basement bathroom, and one of the things I want to do is put in insulation in my subfloor. Currently the subfloor is the slab (house was built in '67). My original thought was to put in 1" extruded polystyrene insulation and 3/4" ply on top, and then tile ontop of the ply. However, looking at the spacing in my basement, I would really rather save the extra 3/4" for headroom. Esp in the shower, where I want to have an overhead showerhead.

Can I lay down Dietra right over the insulation and tile directly on that, or will the insulation be too soft to use as a subfloor?

What about in the shower? If I am building a mortar bed to slope towards the drain anyhow, can I put the mortar bed directly on the insulation, or is that not recommended?

If not, what is the min thickness of ply I can use? 1/2"? 3/8" Does it make a diff whether I use OSB or ply?