Well prime is just going to treat your tap water. You could use it to try to get rid of nitrites in emergencies, but I think it’s better to just keep up with regular water changes and keep an eye on levels. Adding chemicals to your tank isn’t a good idea unless you need to treat sick fish or de-chlorinate tap water.
As for the reason not to add the fish right away; you just started a cycle, a cycle meaning that one substance is going to live off another substance, and so on. This is a three stage cycle. Right now what you are trying to do is get the ammonia to a high enough level so nitrites will start to break them down. When your ammonia level starts to decrease by its self, the nitrite level will increase. Once that begins the nitrites will start to be eaten by the beneficial bacteria a will cause nitrates which is the less toxic to fish. Once all of this has finished your tank has now been cycled, meaning your tank has a fully functional bacterial colony that will help filter the excess waste of your fish.
Why not to add fish quickly? It will increase the bio load on your tank. This will cause your ammonia levels to spike first, then your nitrite levels. When adding more bio waste into your tank without the beneficial bacteria to devour it, it starts to decompose adding to the toxic levels of your tank, some fish are hardy enough to be able to live thru it, some fish aren’t. Even though your tank might seem like its fine, adding two or four fish could really screw up the cycle process and prolong it. I’m telling you this from experience it’s better to wait to add fish, rather than to watch a tank with cloudy white water for three to six weeks.