Coccidia is a microparasite (a protozoa) so it's not like a virus where they have an incubation period and then get sick. It's an illness that builds gradually if the coccidia load is greater than the immune system can keep in check. It is not the type of illness that would cause a healthy kitten to suddenly crash and die. If death did occur, it would be as a result of prolonged diarrhea that stripped the body of fluids, electrolytes, and nutrients over an extended period.
As a cause of death for these kittens, I would strongly look to something other than coccidia (even if you had a fecal run and you know for sure that they did have coccidia). It would be very unusual for coccidia to kill kittens that old, especially if you lost most of the litter. Losing one kitten who was sickly from the start would be less odd but that doesn't seem to be the case here. Coccidia can be fatal to very young or debilitated kittens but for adults and older, reasonably healthy kittens, it's not much more than a nuisance if that.
Coccidia is most likely to be spread through the litterbox and it is resistant to bleach. However, healthy adult cats have strong enough immune systems that they rarely get coccidia infections (and if they do it's easily treated with a course of Albon), so if you know for sure that this is coccidia then it is reasonably safe to introduce him to adult cats and older kittens.
Albon is the most common drug used to treat coccidia but it has a disadvantage in that it does not actually kill the organisms, but merely prevents them from reproducing. The immune system and the organisms' natural life cycle have to do the rest. What this means is that you often have to treat for a long time (up to a month or more) and if you get a litter that is already very debilitated, Albon may not work fast enough. For these guys, there is a new drug called Baycox that actually kills coccidia. It's very expensive, though, so not normally the first choice for basically healthy cats and kittens.
But for your situation, I think it is almost certain that you have something other than or in addition to coccidia going on and it's important to get to the bottom of it as much as possible. I would definitely recommend having a vet do a necropsy on one of the dead kittens and having a fecal and bloodwork run on the surviving kitten to get some more information.