Do I have to be a resident of the UAE to own a .ae domain?
.ae is an unrestricted domain extension. Anyone from any country can register and use .ae domains.

I won an auction. Are there any fees to transfer the domain to my ownership?
You will need to initiate a domain transfer to the registrar of your choice to take hold of the domain you won at auction. AEserver charges approximately $35 and will extend the registration period of your domain for a year.