my sister's cat

I am writing this for my mom and sister who have a rescued cat who is unwell.

I was hoping to get some help from John Stanton..I told them that you're helping with me and my dog as well.

So the cat looks very sickly...as though she does not groom herself. (But my sister thinks she does.) her hair resembles that of a cat with thyroid or kidney issues.

Mom says she looks like it is somewhat painful for her to sharpen her claws. Looks like the stretching up of her legs may be painful. Also her dew claws continuously grow and curl around into her paw pad.

Her age is unknown. The local vet thought she was around 1-2 years but very emaciated/dehydrated for an extended period of time before being rescued. However my mom says she has quite a few "elderly cat" characteristics.

She has an irregularly shaped skull, for a cat.

She is constipated constantly, and her stools are hard as a rock. She frequently poops outside the litter box due to distress of constipation, I believe.
She sleeps a lot. Not very active. She's an indoor only cat (coyotes outside!).

Sister says she vomits frequently. Sometimes several times a day, and then some times she'll go up to a week without vomiting.

Sister has observed that she seems to vomit less when she has been cuddled a lot by her. Which she is VERY cuddly/affectionate towards my sister primarily.

She prefers to sleep in a very curled up position.

She has another cat in the home that is a bully to her, and she is very afraid of him. (He is a rambunctious young male kitten...who is very naughty. lol)

Thanks in advance for taking a look at this!