The short, white worms are likely tapeworms. I would take a sample of them and stool to your regular vet for positive identification and treatment. If they are tapeworms, then your cat either got them from ingesting fleas or from eating an infected rodent. (Tapeworms are not passed from cat to cat--they have to go through an intermediate host).
If your cat never goes outside, then fleas are a possibility and could explain the hairloss. It only takes 1 flea bite in a cat with a flea allergy to lose fur. Generally the fur loss is along the lower back/tail
head area and there may be scabs
along with it. But I would get rid of the worms and treat for fleas first and see if that helps his fur.
Other possibilities for the hairloss are allergies to something other than fleas--pollen, house dust, food
, molds, etc. There could also be a ringworm
problem, although I would think some of your other cats would show symptoms, too. Alternatively, some cats have a behavior problem, like being overly anxious, in which they will pull and lick their fur excessively until they are almost bald. Both allergies and behavior tend to show hairloss in simliar places. When I see a cat with hairloss, I will first try a steroid injection to see if that helps. Depo-Medrol is a steroid that will last about 2 weeks. You can't always see hair regrowing after that amount of time, so sometimes I will give 2 injections before deciding if it is helping or not. If the steroids don't change anything, then I might consider using a behavior drug, like amitryptiline, to see if that will help.