Best way to prevent illness spreading?

I need some advice!
I rescued a 6 week old stray/feral kitten recently. He has worms and has been sneezing and runny eyes. The vet wormed him but they could not test him for FIV and FelV because he was anemic and they could not get enough blood, so I have to bring him back in a week.

The problem is I'm worried about the worms and whatever else he may have spreading to my own cat (or to my dogs or me in the case of the worms) and I don't know what to do with the kitten to prevent this.
He is in a cage which I just cleaned with a bleach solution today but he needs to get out of the cage for socialization. The problem is I'm worried about him spreading his illness to the surfaces of the room... My cat is kept out of the room he is in for now but since I don't know what he has I don't know how long it would survive on say the carpet or other surfaces and possibly later infect my cat. So I'm not sure if I should just keep him confined to the cage and not allow him out into the room until he has been tested and treated for whatever he has? Or what else I can do to keep my own cat healthy (as well as my dogs...)

Viruses can live for a couple weeks but most of them are easily destoyed by disinfecting. If your other cat is an adult and has had vaccinations it should be relatively safe as long as you keep them seperated.

Leukemia is spread by direct contact so keeping them seperate is a good idea. Viruses are air born but most adult cats have the immunity to fight those off or if they do get sick it is usually mild. I would still try to avoid this by keeping them seperate and I usually block the bottom of the door with a blanket.

I had a stray kitten this past summer that was very sick and I kept it seperated with a blanket covering the bottom of the door. Non of my cats ever got sick. But I was very nervous they would. The kitten was here a good month before I found someone else to care for it. AFter it left I disenfected the whole room as best I could.

I always quarantine newcomers for a while - a week for cats, a month for birds (there are more diseases that birds can carry while remaining symptomless). It makes sense to take sensible precautions, especially if you don't know a cat's history and you're waiting for tests. In your case I would suggest quarantine until you can get the newcomer tested for FeLV.