It's never happened with MusicBee but I've had oddly similar problems with other programs in the past where a crash has happened and they've not been able to open again, it's not the ideal solution but because I keep a very lean computer and very frequent backups I went the nuclear option and just clean reinstalled the OS to fix it.
However that's quite an extreme solution which leads me to if you download the portable version of MusicBee and install it to a folder see if that opens up ok, if it does, it's probably a problem with the MusicBee install/library, if it doesn't it's probably a problem with the OS or another program, to see if it's another program start the computer in safe mode and I'd try and open the portable version again, if it doesn't open it's definitely an OS problem.
As for your other questions properly uninstalling MusicBee should not affect your library as your library should be in *user*/Music/MusicBee which a clean install of MusicBee should pickup, to be safe though you can always copy that library folder as a backup. That way you can clean install MusicBee and even though you may loose your layout your library (assuming that's not the problem) should be safe.
If worst comes to worst and some of the library files have broken/corrupted, inside the MusicBee library folder are your playlists which if you had to completely start again you should be able to import those in and at least not loose your playlists.