After copying my files from my old home folder to the new one, the applications menu is now missing categories, and not displaying all installed applications. Is there a config file I should delete somewhere/a way of resetting the applications menu?
GNOME application categories are stored in
/usr/share/desktop-directories/ and in
/home/[your-username]/.local/share/desktop-directories/. Try copying the contents of these folders from your old installation to the new one, and see if it helps.
More info on categories available here.