Apps crash without external display attached

I think reinstalling the OS was a presumptive step. You typically reserve that for system-wide issues, which are isolated/diagnosed by first testing in another user. You will likely find that these issues are unique to your particular user account in which case a clearing of the ~/Caches folder and the relevant files in ~/Library/Preferences is likely in order. The relevant files, would likely involve com.apple.Finder.plist, and com.apple.Safari.plist, possibly also the preference file relating to your display settings. These and other steps are outlined here.