The area around its private parts is raw, the surrounding fur is all gone, and there’s a lump inside; the body is losing fur in patches.

Hello, from the photo you uploaded, the cat’s skin around the genitals is raw and bald, which is mainly considered to come from bacterial infection, so clean and treat the area with anti-inflammatories. At the same time, be alert to pyometra (uterine infection). If possible, take the cat to a veterinary clinic for further diagnosis and treatment. If a clinic visit isn’t convenient, first clean the area with saline, then give an appropriate amount of oral anti-inflammatory and apply a topical one, and put an E-collar on promptly to stop licking. After that, watch whether the symptoms ease; if not, get the cat to a vet as soon as possible.