No they dont have any storage room available at the studios entry point. Better arrange you luggage at some hotel desk or hotel luggage room only.
No, I don't believe so but all hotels allow you to check your luggage with them should your room not be ready.
There are two locations where you can store luggage. One at citywalk across from the Dodger's store and the other is at guest relations which is to your right after you go through the turnstiles. If your luggage is big it's probably best to take it to guest relations.
I think universal has lockers. But it's good to check your luggage at your hotel.
Thanks! Your answer is awaiting moderation.