Maybe it is better to use separate profiles for each OS and create symlinks or hard links to the sqlite databases that you want to share.

Your Linux profile may be using extensions (e.g. Ubuntu Firefox Modifications) that modify specific settings and in such a case you can't really prevent this.
You can use a user.js file to initialize specific prefs on each start, but that makes it impossible to make changes on the about:config page that last the current session and you need to remember which prefs are affected.

Thanks, that's helpful. So a follow-up question: I keep disabling ubufox (the ubuntu firefox modifications extension) and yet it seems to get re-enabled periodically without my consent (possibly it happens at version updates, but I haven't done a controlled test). I was suspicious that ubufox might somehow be responsible for the above problems (at least #2) so I wonder if you know a way to permanently remove ubufox rather than just disabling it?

That can happen if you switch from the Windows OS back to Linux.
That will cause a lot of files to get regenerated because a different Firefox is using that profile (compatibility.ini).
There are also files in the Firefox Profile Folder that store direct links that aren't valid for another OS.

thanks for your help. I'd prefer to avoid the hard/symlink solution, but it's sounding like there is no other way. I did remove ubufox using synaptic (not sure why I didn't think of that to begin with) so at least that problem will go away. I'll repost here if I end up finding any alternative solutions.