Mold around bathroom tub
I recently discovered that there was mold behind the plastic shower surround.
I decided I'd take the opportunity to tile around the tub, so this morning I ripped off the surround and cut out the drywall in the appropriate places. The mold was around most of the tub. I have a few questions.
1) There is little bit of mold on one of the studs (see photo). From searching, it sounds like it'll be okay if I spray/scrub it with a mixture of bleach and water. Does that sound right?
2) I think I'm just being ultra-paranoid but it also sounds like this mold can lead to dry rot in the wall. I don't see anything obvious, but I wanted to ask anyway just to cover all my bases.
3) There is a door next to the tub (see photo). I cut the drywall an inch from the door moulding, where I was going to overlap the tile. But, just above the tub, there is mold on the drywall that goes behind that door moulding. I can't exactly get that part of the drywall out without taking off the door and a piece of the moulding. Is that something I should do, or will it simply die off if I spray it with the bleach/water mixture?