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)

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).

• Uralic Languages (a reasonably modern survey on all of the languages with some coverage of the history of most of the languages)
  
• The Uralic Languages: Description, History and Foreign Influences (expensive collection of essays on the languages which sometimes touch on non-linguistic aspects)
  
• Early Contacts between Uralic and Indo-European: Linguistic and Archaeological Considerations (this could be up your alley but note that this doesn't consider "Uralic archaeology" on its own merits but rather its contacts with I-E) (you can get probably a certain taste of this book's content in this essay by one of the co-authors of the book, Asko Parpola who isn't a linguist or even focused on Uralistics at all. He's an Indologist (!))
  
  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):
  
  
• Linguistica Uralica (Estonia)
  
• Suomalais-Ugrilainen Seura (Finland) (several journals published)
  
• Nyelvtudományi Közlemények (Hungary)
  
• Ежегодник финно-угорских исследований (Russia)

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