Hi there. Thanks for the question. Let me see if I can help
Is there any swelling down there that you can see? Redness of the skin on the belly or back by his genitals?
There are a couple of things that may be of concern:
1. anal gland impaction: although not as common in cats as in dogs, it does happen. He may need to have the vet check and express his anal glands. When they get impacted with material they get very irritated
2. Allergies: Especially if the skin seems reddened and very itchy, he may have food or environmental allergies and so the biting, licking, pulling hair is because his skin itches. Then because he is ingesting a lot of hair, he may have a hairball and this is messing with his appetite. This might be something to discuss with the vet. You coudl try a steroid/antihistamine shot if your vet thinks this is a possibility as it is obviously very hard to control the allergen exposure of an outdoor cat
3. Urinary Tract Infection or bladder stones or a stone stuck in his urethra (blockage): he would likely be acting very sickly if it was this. Lethargic and inappetant. Maybe straining to pee but nothing coming out. Sometimes their bellies are very tender. This would be an emergency situation...so if his symptoms match my description, get him to a vet right away.
I hope this helps. Best of luck