Obviously it depends as well on how the opposition is playing the ball out. If the ball is played wide then whoever is nearest will be the first to react.
Not necessarily and its one of the hardest reasons its difficult to see who initialises the press. Often if the ball is played out, salah say will jog over with not much effort, but mane, firmino et al will have pushed up on the passing options, salah then burst towards the defender and he's suddenly got nowhere to go but kick it long. Its a well oiled machine, with everyone playing there part. Last night we saw an aimless press, the nearest player running toward the ball, but that just leads to an easy outball.
Probably makes sense for the opposition to avoid Salah when playing out too; quickest acceleration and most deadly attacker too.