Rescue with odd coat

In the pics below, you can see the coat is kind of balding in spots. I know she's a Rex, but I'm wondering if maybe her balding and uneven coat is because of a bad diet. The people who gave her to me, gave me the cage she and her cage mate were living in(nice cage), along with two bags of food. 1 unopened and 1 that they were almost done with. The one that they were almost done with, obviously what they were feeding them was actually a gerbil & hamster mix. Not really good for rats at all. What I'm wondering is her coat this way because she's a Rex or is it cause from a bad diet. I don't use store bought mix, I make my mix from organic(only seeds grain and nuts), and at night they get raw organic veggies and cooked pumpkin, chick peas, meat etc. Absolutely no go's. I know not everybody is as neurotic as me about what their rats eat, but diet can make or break rats health. And since I'm new to being a rat mama, there are probably a lot of things I can't spot in just a look. So I come to you for help! Thank You

How are her whiskers? If they are slightly curly, then she's a rex. They don't look entirely straight to me in the pic but it's hard to see.
As for food, keep their proteins low. I'd cut out the meat, they really don't need that. The Chiny Study has proven that rats do far better on very low protein and low fat.
For 15 years, I've fed my rats a high quality commercial diet of either Oxbow or Harlan Teklad 14% protein. I've had very healthy rats and quite a few lived to well over 3 years. You are right that diet can make or break their health but some commercial diet are really good.

Other reasons for patchy fur is too high protein diet, mites/lice, dermatitis, barbering.