I see a lot on here that there is a fee for surrendering cats. If I do this, is she going to be taken care of and find a new home? Does she run the risk of being put down?

You will need to contact them on that info one question you can ask to make sure she is not put down is what are there policy on time frames às to if they rotate and send to a shelter or pound if they are not adopted. In a certain amount of time.

You need to call them first and see if they will take your cat due to limited space issues.

Honestly our Az. Shelters are so overwhelming packed they have been Euthunizing to make room . Its detrimental that Most all Rescues intake is closed. Sun Valley Animal Hospital is a vet not a Shelter . Please go to StraydarAzLostfound,Rehoming &Adoptions sign up it's free on FB . The group can help with Rescues you can begin searching for any recommendations . Good luck