altho blind elk's car (R32 GTS4 with RB25DET froma stagea) is proof that it is possible...
I've costed the whole thing up (down to sourcing and shipping a Laurel halfcut in one of our containers, and doing most of the engine swap work myself) and even at minimal cost, it was far easier and cheaper to get rid of the GTS4 and buy a GTR.
You have to remember that Stagea or Laurel engines (ie AWD RB25DET's) don't have aftermaket tuning support like power FC's etc. Also R32 RB20DET's share a lot more with RB26DETT's than they do with RB25's as they were both designed around the same time (ie with injector positioning etc). So naturally the logical thing to do is to put an RB26 in if you're gonna do an engine swap.
The ENR33 has similar gear ratios to a NC34 (stagea or laurel AWD RB25DET), wheras the BNR32 and HNR32 have different ratios again.
So at the end of the day I strapped a HKS2530 to my RB20DET, and enjoy my GTS4 for what it is, a fun getaround car that can switch from AWD to RWD at the flick of a switch. If you want a powerful AWD car... buy a GTR, if you live in teh snow and want something that won't bog down, buy an R33 GTS4.
To answer your Q's:
Question 1:
Yes
Question 2:
Yes
Question 3:
around 3k minimum, 6k if you don't have a workshop and work for an import company
Question 4:
not any more than a more easier and cheaper RB25DET powered R32 GTSt. R32 AWD is about as useful as tits on a bull, unless you're into drag racing and towing stuff.