After I type in the name, I'd like to be able to press my 'Enter' key to achieve the same result as clicking the apply button. This would speed things up tremendously.

Agreed - will add in next designer update.

15/11/2009 Designer - Allow enter key shortcut to Add territory button

This would be nice if it was the same for Adding Continents (especially handy if you have a lot of the same values).

Yes, as much as can be done without using the mouse is ideal.