Conqueror's doesn't mean wanting to conquer something, but being above others at something. Zoro obviously wants to be above all swordsmen in strenght, so that's that, and Akainu believes in absolute justice and hunting down pirates, so in a way he wants to be above all pirates.
And yes, you have it or you don't, but you can awaken it at different times of your live, Doffy did it as a kid, but Luffy only found out about it when he was 17, so Zoro and Akainu could still awaken it.