Hello Niels, thank you for your post and welcome to the forum 
First off, regarding your questions:
- Haven’t seen reports like this, but the issue seems somewhat similar to the discussion here: Cannot delete fontbase font folder
tl;dr: it’s possible some system fonts were copied into folders synced with FontBase, and even though FontBase itself is not blocking them in any way, the OS things the user is trying to delete a system font. A possible solution could lie in copying the relevant fonts to a safe place, uninstalling them from the Windows/Fonts folder, removing the unwanted extra copies and then installing the copies stored in the safe place mentioned above. - Hopefully other forum members will weigh in on this as well. The shouldn’t be any difference between OneDrive and Dropbox (with offline file access enabled) in this respect.
- Your setup seems to fulfill most of the best practice criteria already. The only things to improve could include making sure no system fonts get into FontBase-related folders (for reasons mentioned in answer 1) and making sure FontBase is always started after OneDrive is fully started and functional, i.e. preferably refrain from setting both of these apps to auto-start on system startup, as this could result in a situation where FontBase is already working while OneDrive is stil loading, thus confusing FontBase as to font file availability and making it think files were deleted, when in reality they will be available shortly.
Based on the tests you’re already performed this shouldn’t be a file access conflict with FontBase, as closing FontBase and restarting the system eliminates any potential locking/access on the part of FontBase until it’s restarted.
Thank you again,