Can I put an InDesign file for review on a local network (not in the Adobe cloud)?
Only as a PDF file. Post the PDF on your local network. Depending on what version of Acrobat or Acrobat Reader the other users are using, you may need to enable reader extensions on the file by choosing File > Save As Other > Reader Extended PDF > Enable More Tools. They will then be able to comment and annotate on the file.
and such a file will allow several people to work at the same time?
Not simultaneously but linearly, yes. One person could open the file, add their comments, then another, and another. But you can't open the same files on multiple computers at the same time without Adobe's cloud services.
it is very helpful,
please confirm if i think right, if i need quick comments from e.g. 5 people, it would be most effective to export 5 separate PDFs and then import to InD comments from 5 different files?
Actually just make one PDF and send to each person.