Why was Memnon, an Ethiopian King, involved in the Trojan war? And why is he identified as the father of Thor in the Prose Edda?

We do not know for certain why Snorri wrote of the ancestry of the Æsir like he did, but I can provide some context.

First, there is the term euhemerism, which is the idea that religions have origins in real people. This was a very widespread idea in the middle ages to explain why heathens existed, and is the perfect term to describe the Prose Edda. What you are specifically referencing is in the prologue, where it is explained that the Æsir where actually Troyans(or at least vassals of them), who ended up emigrating to the north, where they would be worshipped. This is not the only reference to Troy, as in Skáldskaparmál, the Norse myths are explained as allegories of stories from the Trojan war.

Why this fascination with Troy? Snorri's Edda was written at a time, where having Troyan origins was the best you could get. There was a long tradition of tracing ancestry back to Troy, and Troyan "history" was some of the most popular in the Middle Ages. This was no different in Iceland, as we can see from Snorri, and also that eventually a book on the Trojan war (not the Illiad, but instead "Daretis Phrygii de excidio Trojae historia". A full version of the Illiad wasn't known at the time, and was also considered an unreliable source, as Homer was greek) was translated into Icelandic as the "Trójumanna Saga".

The Prosaic Edda is therefore very much in line with mainland European traditions of the time, and is very much a christian work, that really tries to underline the point that none of the stories it tells were true, or at least that they did not happen in the way the oral tales told. Whether Snorri believed Thor to be the son of Memnon is what we cannot know, but I don't know of any sources that could have given him that understanding, other than hearing/reading the stories of the Troyan war, and thinking they sounded familiar. An alternative, is that he created the euhemeristic narrative to make sure not to seem pagan, and that it was pure invention. In any case, Thor having a Trojan origin was prestigious, so it is no wonder that that is the conclusion he reached.

Sources:

Specifically for Euhemerism in scandinavia (and Iceland), read Jacob Hobson's “Euhemerism and the Veiling of History in Early Scandinavian Literature”

For a very old source on the idea of Euhemerism in medieval litterature, John Daniel Cooke's "Euhemerism: A Mediaeval Interpretation of Classical Paganism" from 1927, is perhaps not the most up to date, but is what I used when researching it at university.

On Troy, most of what I know comes from Stefanie Würth's chapter "Historiography and pseudo-history" in the amazing "A Companion to Old Norse-Icelandic Literature and Culture", edited by Rory McTurk. Her reference list is probably the thing to look at for more on the topic.