The Explorator comes with a servo-skull, now he is about to recieve a Grapplehawk as a gift. Can he use them both at the same time? Furthermore, how do these work in combat? Do they roll initiative as the rest of the characters, or are they controlled at the Explorator's turn?
They act on their own initiative to commands you give them (Command/Tech-use as per rules/the GM). If the GM prefers to simplify, they can act either at the end of your action, or the end of the round.
As long as the requisite commands are given, I see no reason why you couldn't use both at the same time. Giving differing actions will take additional effort though ("All of you, initiate combat macro delta" is a command that can be given to multiple units easily, whereas "You, attack them and you, heal him" is two separate commands that takes longer to convey.).
It's also up to the GM whether that necessarily constitutes an action to issue the command. It's probably technically a half-action to give a command to a subordinate (no rulebooks to hand), but some handwaving can be done for regularly repeated tasks (if your servo-skull is preset to heal someone when it sees they've been cut open, then you don't need to make a separate command for that action).