“Europe slowly regressed into nomadic huts” ? There was certainly a regression in the material culture of post-Roman Europe (as forcefully argued by Bryan Ward-Perkins), but this period of “nomadic huts” still produced many buildings that sound strangely un-nomadic (cathedrals, palaces, this kind of things). More generally, though there were migrations and displaced populations during the breakdown of the Roman Empire, the economic system of Europe was never disturbed enough to prompt a “reversal” to nomadism.

The Church never acted as a governing body as such; during limited periods of breakdown of the central power (among which the 5th century, e.g. in Gaul), bishops often acted as the central figure of a city (but it was not the Church as a body, rather the bishop as a local magnate), but some sort of secular authorities always took the reins after a limited period of time. Then, the structure of the Church was also used by kings as a form of administrative/para-administrative support (to be really schematic), but the Church never governed Europe, even less formally.

I therefore have the feeling that your vision of medieval Europe is quite, well, incorrect, and that your question stems from very serious misconceptions of the nature of the period between 500 and 1500. I am not a historian of science, so I am not really well-armed to answer your question (though it is important to note that many of the things you mentioned disappeared not because people did not know how to create them, but because they were not needed: for instance, the need for aqueducts is created by big city centres, that did not really exist anymore in Early Medieval Europe) but to take a single example, glass-blowing did not disappear after that “Rome fell to the Germanic tribes;” it was certainly alive in Carolingian Europe, though not as impressive as it could be in the heydays of the Roman Empire.

I know that Europe rediscovered Aristotle and the like through the Muslims

This is also a really annoying misconception. Europeans knew of Aristotle all along. They knew of Ptolemy. They knew of Xenophon and Julius Caesar and Cicero. Byzantine scholars archived, debated, expanded, and critiqued these works 500 years before the Renaissance. In my opinion, the Muslims get too much of the credit when talking about "intellectual revival" in Europe. They played a role, but they were not the only ones who ensured the survival of these works.

I'll give you an excerpt from the Suda, a Byzantine encyclopedia dating from the 10th Century, which highlights their knowledge of the philosophical figures of old:

Aristotle: Son of Nikomakhos and Phaistias. Nikomakhos was a physician in the tradition of the Asklepiads, from Nikomakhos the son of Makhaon. Aristotle came from Stageira, a city of Thrace; he was a philosopher, a disciple of Plato, and was a stammerer. He presided for 13 years over the philosophy which was called Peripatetic; it acquired this name because he taught on a walking path peripatos or in a garden after he left the Academy, in which Plato taught. He was born in the 99th Olympiad and died by drinking aconite in Chalkis, because he was being summoned to receive punishment, since he had written a paean to Hermeias the eunuch; but some say he died of disease when he had lived 70 years.

I mean, Rome had indoor plumbing, dams and aqueducts, even glass-blowing in the first century and when it fell to the Germanic tribes, Europe slowly regressed into nomadic huts.

The Byzantines had indoor plumbing, dams and aquaducts, and glassblowing in the 10th Century. None of this stuff was lost to them. It is a terrible and common misconception that the Roman Empire fell in AD 476 and all of sudden threw all of Europe into the "Dark Ages". Byzantium endured, Empires were rebuilt in the West, and technology and literature survived. The people who lived during that time were a lot more developed than conventional understanding gives them credit for.