Reddit reviews The Uralic Languages: Description, History and Foreign Influences (Handbuch Der Orientalistik Achte Abteilung Handbook of Uralic Studies Vol 1) ... Asi) (English, French and German Edition)
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The melding of several disciplines whose common thread is that the subjects/speech communities speak related languages is a sign of how advanced (or less charitably: oversubscribed) Indo-European studies are compared to studies of other languages. For Uralic languages, it's just nowhere close.
You'll probably need to read several books or monographs involving Uralic languages and the speech communities to get some semblance of an answer to your questions about the history of the ancestors of today's Finns, Estonians, Hungarians, Saami, Udmurts et al. It won't be found in a neat package (nor is it necessarily valid to infer that linguistic affinity suggests that the speech communities can be then homogenized or abstracted into some cohesive group - excepting perhaps for speakers of Proto-Uralic, and even then this is tough to gauge).
In the end, you might have to go trawling for stuff in academic journals. Try your luck with the following (N.B. not all of the articles in these publications are in English if that's the only language you know):
Print. They are:
https://www.amazon.com/Uralic-Languages-Routledge-Language-Family/dp/0415412641
https://www.amazon.com/Uralic-Languages-Description-Influences-Orientalistik/dp/9004077413
https://www.amazon.ca/Survey-Uralic-languages-B-Collinder/dp/B0006C1E3E
There's this pdf, too:
http://www.helsinki.fi/~tasalmin/SW.pdf