I've painted before (OK, only 2 small closets on my own, pulling out the useless wood shelves and installing closet systems; my friends took over painting my kitchen a few years ago), but I have some technical questions for you.

I'm repainting the interior of an upstairs-level laundry area (which is in a closet) because it's looking really dirty, it's the previous owners' color (apricot) and I just want a clean, white wall, and because I had another shelf installed so it makes the current state look even worse. (first photo should be a general shot of the closet interior)

Here goes:

1) How do you know if the paint that's on a wall now is latex-based or oil-based? My friends got a surprise in the kitchen when they realized it was an oil-based paint. I vaguely recall running to the HD for a suitable primer at about 10 pm. But is there a test so I'll know what kind of primer to use? It's unlikely the previous owners' painters used an oil in there, I concede.

2) The nails used to install the 2nd shelf weren't countersunk, and I just realized it now, months after the install. When I do the spackling part of the prep work (I'll need to do a little touchup on the walls from previous nail holes), will the metal repel the spackle?

3) I can't see any evidence that the shelves were nailed in all around the support pieces of wood beneath them--I think they're nailed down only on the sides. So in the close-up photo, you can see the gaps in the corners. I can try to hammer some more nails all around, but since the shelves aren't sagging, is the easiest, good long-term solution just to caulk those gaps?

3) And what's a good alternative to TSP to use to wipe down the dirty top shelf and the walls?

Here is a link that might be useful: