Nailed it for you.

A very quick and inexpensive alternative:

The three or five piece shower/tub liners. Their advantage is that you only lose the bathroom for one day.

I'd not worry about the mold overmuch, turns out black mold doesn't cause the harm it was said to - another one of those scares. Just spray everything down with Lysol, thoroughly.

The studs will almost certainly be ok. If not, don't remove, add. Mold and mildew resistant backer board is the way to go - whether it's the blue board drywall or (my strong preference) cement board. The rest Mike told you. Here's a link to the liners - we've done 10+ shower/tubs with them the past few years and had no complaints, just call backs to do another shower in the basement of two of the houses where we'd done the liners.

The link is to an inexpensive one. The sky is the limit and some are so designed you have real trouble telling they're not tile, thick and really well structured.

and timeless. I've seen Kohler doors hold up quite well in a friends' house - and she has a constant stream of kids, grandkids and now great-grandkids through there all the time.

Our local Homeless Despot master plumber (the real deal) dislikes the American Standard, says their finishes fail too fast. Only done two Delta doors, both repairs and both times they couldn't have been nicer or faster sending the parts. They, too, seemed to have some finish wear which I haven't seen on Kohler. Just, I've not enough experience to say whether that's due to poor cleaning (like using toilet bowl cleaner) or less than perfect production quality.

If you don't mind my two cents, here's what I'd do:

1) Get the fan problem solved. Until the air is moving, everything else is for naught.

2) Nearly all liners (even the inexpensive ones for around $100) also have window kits. It's no big deal, easy to do and let's you keep the window/light/air while getting the job done in one day.

3) Unless the bathroom is the size of a football field, it's more important that their be no standing air pockets than that the fan be right over the shower. Personally, I always cringe when one is directly over the shower - and won't take on the job unless an electrician has GFCI'd the damn thing. I mean, electricity and flowing water and wet, naked people and copper here there and everywhere - what could possibly go wrong?

Made and I remain convinced that what isn't there to fail can't fail.

Clearly, you're right about proper dimensioning the fan and the need for proper ducting.

Still and all, it's better to do the job right, once than to keep on fighting with it.