I am wondering why the races of Tamriel have not figured out how to use Dwemer Technology to give themselves things like working plumbing and other pieces of technology.

Dwarven ruins seem to have been studied long enough.

Ever since the 1st Era technology has been gradually degrading. The early Alessian empire was at a level of technology that was likely comparable to the late Iron Age on earth, and to them, the medieval style armor of Pelinal was considered incredibly futuristic. The Dwemer were alone in their great advancement of technology, their knowledge of the universe being well beyond that of most other mortals (not necessarily a good thing, what with the Numidium and such) Two thousand years later, during the Reman Empire, technology had progressed to the point that both the Empire and the Altmer had space programs and moon colonies. But then things got in the way, and during the 2nd Era technology had decayed to about the point it is at now, and its stayed at about that level ever since. Sure, there have been some advancements, the Empire rediscovered airships and crossbows, though never to the point of widespread adoption, and of course there are various Telvanni who redeveloped Dwemer technology, but of course the Telvanni aren't much into sharing.

So in short, yes, much of the Dwemer's technology has been rediscovered and even put into working order, but there is simply no good way to mass produce most of it for wide use.

Also there is the simple matter that the Dwemers technology wasn't based on pure mechanics alone, much of it had a magical component, and the Dwemer took that knowledge with them when they disappeared, as well as the technology to make their fancy metal that apparently is immune to rust and decay.

And a note about plumbing, based on the number of sewers we've had to slog through in the series as well as the various working public fountains, I think it is safe to say that Tamriel, or at least parts of it, have plumbing, not our fancy modern plumbing, but reliable 1st-century-roman style plumbing. The main reason we don't hear much about it is because, honestly, plumbing is just one of those things that is assumed to exist, but never really shown, because frankly Bethesda just doesn't want to go into detail about how the people of Tamriel deal with their fecal material.

The game Battlespire features an Imperial space station in use as a training facility in the late 3rd era, during the time of the first TES game. (although it had recently been captured by Daedra).