One question at a time..........
First off...leave the drywall. Build out from there. The details will kill you if you remove the drywall and try to get everything in plane from the studs.
That said, 3/4" rails and stiles applied to drywall with 3/8" beadboard fit inside?
A nice 5/15" stop molding will work nicely to cover the cuts.
The rabbet gives it more of a Shaker look.
It depends on the look that YOU want.
Next on your diagram you show 1x6 with filler and baseboard on top of that.
It can tend to get a bit Clunky especially when you turn corners of die back onto itself.
This is 1x6 top rail with 1x8 bottom rail and shoe molding. The top rail looks narrower because the cap and apron cover 1-2" of it.
Applying the rail over the drywall gives you plenty of nailing for the cap
Diagrams - I liked the 1st diagram of the multi height wall.
Hope this helps..........
edit: and Joe beat me to the punch on the Drywall