Do the characters evolve in the game Pokemon Mystery Dungeon: Blue Rescue Team?

Answer 1

yes, but not until AFTER you beat the storyline of the game.

when you do that, there will be a stone called "the voice" that will evolve your pokemon.

for pokemon that needed to be traded in the past -like gengar- you need to talk to the stone while holding 'link cables'

for moves that higher forms learn that younger forms don't (like charizard learning wing attack at level 36) you can easily go to gulpin to the SE of the town square

other than that, you can only recruit pokemon that are already evolved -like getting a houndoom instead of a houndour- but you need to be quite a high level in order to do that. we're talking like level 90 or something, for MOST of them