Thanks for quick response, and tips, - but:
I trashed prefs, - not better ...
Removed and reistalled Indesign, - same problem.
Turned off TypeKit, - was allowed to open document, but same crash when trying to change fonts (local fonts, - not in TypeKit) in the document.
Managed to open the doc without crash, saved as idml-file, and opened that file after restarting Indesign. This time I was allowed to change the fonts, and it seems like the document is working fine, -. for now, at least. TypeKit still off.
But: the problem still exists, so there are some serious problems with the app, and it makes me rather nervous beeing dependent on it professionally.