Is this not ok for a cat?

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Put your cat on a diet. Cats should not weigh 25 lbs. Some cats will eat as much as you feed them, but that is not healthy.

A vet cannot just put an animal down, without your permission.

You could also take the cat to an animal rescue league. Unfortunately, you are not being kind to your cat in overfeeding her. A grooming salon can shave any matted areas.

It's not okay, and the vet will not 'just put her down'. Try feeding her less.

Buy a Furminator brush and brush her DAILY.  Help her out.  When a cat's hair gets matted THAT IS NEGLECT!!  

The tumour a need to be removed.

YOU  need to control her diet.

YOU need to brush/groom her daily.

Take her to the vet. Find out about treatment.

Until you know exactly what is involved you cannot make a decision on euthanasia  and if it is needed.

It will only be done without your consent of you neglect her.