That layer of solids at the bottom IS the yeast, with a little trub mixed in that won't hurt anything. The beer above may be cloudy with suspended non yeast matter, proteins, etc., and dead yeast. The proper way to store the yeast is just like that, under the protective environment of the beer it made, in the fridge, loosely covered with foil or a lid that's not screwed on -- some gas will still be produced and could explode the jar if sealed. As you've said, you noticed bubbling. Don't discard the beer, and whatever you read in outdated and misinformed homebrew books, NEVER rinse the yeast with water. This is very damaging to the yeast, invites infection, and there is no need to remove the trub anyway. You'll love reusing your harvested yeast. Not only saves you money, but as the yeast adapts from lab conditions to actual brewery conditions over a couple of generations, you may find it performs better. And one-fourth of the yeast left after fermentation is about the right amount to pitch in the next batch, but I wouldn't recommend saving all four jars. Just use one to start the next fermentation, then harvest one-fourth of that, and keep doing this, serially repitching the yeast. It will be freshest that way, and again, if your sanitation is good, it will only improve; you can get at least five generations out of it if your practices are sound and sanitary and you use it again fairly soon.