Try to sell them on eBay. For those things that you think nobody uses anymore (like the old film camera), you might want to try posting them as collectibles. They may rake in more money than you realize. I've read a recent news about an old Nintendo getting sold for $25,000 to a collector...
25 years is a very long time, the garage floor has already served you well. I'm also leaning towards complete removal and repour to avoid any other problems you can't foresee that might have accrued along those 25 years.
Only by looking at your room can we know for sure what's causing the discoloration. The best solution really is to have a professional take a look at it. You can probably ask an individual contractor to take a look at it without committing to having him repair it.
The wood is probably pre-primed, which is why the instructions tell you not to prime it anymore. When in doubt, you should always follow the painting directions.
Yeah, you need to know what's inside that wall before you go breaking it for your door. You might hit some wiring and plumbing in there and get into more problems. For something like this I don't think it's a DIY project so just ask a professional to do it.
It's impossible, just buy an outswing door. If you install an inswing door backwards you'll get a lefty outswing door, and trying to manually customize it is too much of a hassle to even bother with you might end up breaking the door.
To prevent mold from cultivating in your household, do random checking of your pipelines and basement for leaks and moisture and fix the problems as soon as possible if there are any.