Please do take this cat to the vet immediately, and no more milk. Cats lack the digestive enzymes to break down milk and giving it to her could be making her sicker.
One of my cats is 13, and if she showed any of the same symptoms, she would have been at the vet days ago. 12 is not that old. Many cats live to be 15-20 given the proper care and veterinary attention.
Refusing a cat medical attention just because she's old is, IMO, cruel. Thats like refusing to call an ambulance for your grandma when she falls down the stairs because, well, she probably won't be around much longer anyway.
You've come here asking for advice, so I'm sure you do care about this cat. Whenever a cat stops eating, it calls for a vet visit. Combine that with diarrhea and its an emergency. This is not going to clear up on its own and if you don't do something, your cat will probably die. She is suffering, even if you may not realize it.
If you don't feel the need to spend the money saving your cat, at least bring her to the vet and surrender her into their care so they may do whats right for her and find her a loving caring home.