Will I lose third party apps if I delete user 501? One users account is broken. No apple apps work. Can I delete and create a new user and not lose Registered Apps like Adobe. The problems with the account seem to never end. Fix one another pops up. Made another user to see if it was just the one. All apps work on second user.
Probably not. If you look at your Macintosh HD You should see...

Applications/
Library/
System/
Users/


Typically Applications are installed globally in this top level Applications directory here.

If you look in 

Users/
    |_ MyUserName
        |_ Applications
        |_ Desktop
        |_ Documents 
        |_ Downloads
        |_ Etc Etc.


Hardly ever are applications installed in this Applications directory. 

So unless you see any there. It should be ok to remove the problematic user.