Visitors applying for residence are of a few different types:
- Performers and scholars
- Mercenaries
- Monster hunters
Performers and scholars fart around in the fortress for two years before they apply for citizenship (unless depression gets them first). Once they have been accepted as citizens they're yours to command just as any other citizen.
Mercs never apply for citizenship, but they can be put into militia squads immediately, but each squad has to be led by a citizen.
Monster hunters spend their time eating, drinking, and praying, and may eventually haul their lazy asses down into the caverns (assuming a path to them is open), littering the caverns with bits of fairly harmless cavern critters (luring dorfs down there to clean it up), before returning back up to eat/drink/pray/sleep. Eventually they'll go down into the caverns and litter them with bits of themselves, luring more dorfs to their doom as they try to clean up that mess and encounter whatever dismembered the monster hunter. I doubt monster hunters apply for citizenship, but they tend not to live long enough for anyone to find out whether they would or wouldn't.
I think the default pop cap is something like 220. However, 150 dorfs is quite a lot. Note that the population cap concerns the number of sapient units, while the number of animals goes into a separate pool.
Various things can cause migrants to fail to appear for shorter or longer stretches of time. If your fortress has seen a lot of casualties (of the fortress population, not invaders), that can scare migrants away from your death trap. Another thing thought to cause it is the mountainhome being under siege or something like that. However, there are also quite a few cases of migrants just not appearing for no known reason, and then start to appear later, again for no know reason.