My guess, Molly, is that the black is mildew, the same stuff that grows on your bathroom walls and the cause is the same, water on the walls that doesn't dry quickly. Cleaning it should be fairly easy. A cup of household bleach to a gallon of water should remove most of it and you may want to scrub it with a brush in the tough places. Wear gloves and eye protection.
The next problem is figuring why it wants to grow there. Water is coming from somewhere so check to see if you can get any indication during the next heavy rain. You will have to have some idea where the water is coming in before you can start figuring out how to keep it out. Perhaps there is just a lot of humidity and "dead air" in the room and a bathroom ceiling fan will help, but you want to check for leaks around the roof and walls first.
I think that you might be heading for a mess on your new vinyl floor. The plywood/Liquid Nails will work--for a while. But I think that eventually the edges where the plywood is butted together will start to show. My guess is that a leveling concrete should be put on your old floor first. Try posting at www.floorsearch.com and see what the pro's there have to say.