What you do is you fight pokemon, and they say "So n so wants to be on your team. Will you accept them as a member?" and you say yes, but it only works after you beat the first little story line.
Nope
Yes
You have to complete the game, and then recruit it.
in the second cave
Nope.only in the final maze
concealed ruins with secret slab or mystery part
I'm pretty sure you can recruit magikarp at Lake Afar.
Pokemon Mystery Dungeon Explorers of Time / Darkness / Sky: Bottomless Sea B1F-B49F.
You can not get mew until you recruit mew later in the game
Anything really - continue with missions, recruit legendaries.
dungeon leader can be any Pokemon you recruit. you will be able to change leading Pokemon after you graduate .
no there are not there is an assembely at the guild though where all the Pokemon u recruit will be there