Thank you for your question. My name is***** I have been a small animal veterinarian for 14 years and I'd like to help with your question.
Older cats can develop a few different problems that cause weight loss and vomiting. The most common are diabetes and kidney disease. With both of these conditions you will see that the cats drink water well, even in excessive amounts. But they don't have much appetite, they loss weight. Some of the vomit, some are weak or lethargic. I would worry something like this is going on in your kitty. These conditions don't usually cause any skin problems other than maybe thinner skin. So I would suspect that the biting and scratching are not related to her underlying problem. I would suspect either fleas or allergies that cause the biting, but if her underlying health is poor then the sores that are appearing will be less likely to heal.
The soft lump could be a tumor (either benign or malignant) or an abscess.
With so many different things going on, you really need to take her to vet and get some bloodwork done to find her underlying heal problem and determine if there are treatments that can help her feel better.
You could try to treat the itching and skin problem at home, but without addressing what is causing her weight loss I'm not sure how successful you will be. If she will let you bath her with a medicated shampoo (I like Malaseb which you can get on Amazon.com) and make sure she doesn't have fleas that would be appropriate. But without knowing what is going on inside I don't know if the stress of a bath is a good idea.
I hope that helps, but if you have more questions please let me know.