One user can't open anything after Yosemite upgrade
There is likely a corrupt preferences or other file in the user's ~/Library folder. Honestly your best bet is to create another users folder for that person, copy their files over and set up Mail, Messages, Safari and the like from scratch.

Once you have a working profile you can slowly migrate other things from the old to the new user folder (old Mail folders, Safari bookmarks, etc.) till you have enough restored for everything to work as necessary.

At that point you can delete the old user.