Why was part of the Gemara put down in Aramaic? Why were rabbis in Babylon and Israel speaking in languages other than Hebrew? There is plenty of evidence that Hebrew was still prevalent and known in Gemara times (and, of course, Rabbis would understand it). Why was Aramaic picked over Hebrew? Was it an attempt to stop people from speaking in Lashon Hakodesh?

Of course it wasn't to stop people from speaking Lashon HaKodesh – for to the contrary, our sages precisely encouraged us to speak Hebrew even for our secular speech, saying it brings long life, a share in the world to come, and hastens the redemption (see "The Mitzva of Speaking Hebrew" at https://www.tora.co.il/shiurim/shvat.htm ). The opposition (!) to speaking Lashon HaKodesh which you mentioned, is just a recent anti-Zionist "invention" of the Satmar rebbe, based upon his difficult understanding of a Rambam, which incidentally contradicts the Rambam himself in 3 other places (see there, pp. 15-17). In addition, Aramaic is a step-sister of Hebrew/Lashon HaKodesh. For example, there's a law in divorce, that says that the gett must be written in 1 language, but the classic wording always used, is a combination of Hebrew and Aramaic, proving that they're really considered one and the same. Aramaic, although clearly less "pure" than Hebrew as the Holy Language, was simply the dialect of Hebrew which was used at the time, apparently influenced from the surrounding nations.