My 16 year old cat can't walk more than a few steps, she's not eating or drinking properly.?

omg! That cat is extremely ill. Probably kidney failure. She should have been euthanised by now. A 16 year old cat is very uncommon. Mine was 12 when she started to show the same symptoms. You have got to have that cat put down. She is miserable and depressed. Cats are very social and happy animals. Don't let her go through that agony especially if it is kidney failure. If it is, then she is not able to digest food that is why she is vomitting. It is painful for the cat to eat.