I'll try to answer all the parts of your question:
1. Nebulizer vs Inhaler - at age 3, you are probably much better with a nebulizer, since kids that young have a hard time doing the inhaler properly, even with a spacer. My son's doctors wouldn't even prescribe an inhaler until he was 5. Now, at 7, they still make him use the spacer. The nebulizer takes longer and is obviously more of a pain in the neck, but it definitely delivers the medicine successfully. We always just let our son watch a tv show while he used it so he would sit there quietly.
2. Maybe your son's prescription is very different than mine, but are you saying that you do six puffs of albuterol every four hours, meaning 36 puffs a day? Or do you mean one puff every four hours so 6 total in a day? The former sounds like an insane amount of medicine, but if you mean a total of 6 a day, that is much more reasonable. Anyway, my point is just make sure with the doctor that you aren't giving too much. No criticism intended, simply saying that sounds like WAY more than we've ever been prescribed.
3. Chances are, whenever you decide to return to preschool, your son will get sick an average of once a month for the first year. So, if you want to keep him out this year, that's fine, but I would definitely recommend having him go at least one year before kinder so that he isn't sick all the time as a kindergartener. Most kids get sick a lot the first year they are in school and kids like ours with the viral-induced asthma tend to be a little worse than average. It certainly isn't awful to wait until he's four for preschool. Just make sure you do something before kinder so he doesn't miss too much school when it really matters. It sounds like you're doing really well to keep him involved and socialized in the meantime.