Categories Field Auto-Sort Alphabetically and Mirror between Company & Contact

The categories field is one that I find that I am constantly updating and it's a pain to have to add new categories, then go back into the edit window to auto-sort alphabetically.  It would make much more sense to have an auto-sort alphabetically option so that the second step could be eliminated.  Additionally, I'd prefer to be able to add new categories on the fly when I'm adding a new contact or company, rather than having to go to the settings panel to add the new categories and return to the new contact or company to apply.  

Additionally, I would love the option to be able to mirror this field between company and contacts so that it doesn't have to be manually duplicated.