Having worked in IT, I'm pretty familiar with the phrase "spit out information" and while the second "it" could refer to the info, not the cube, that may be suggesting too much.
Actually, he receives two cubes from the lady, one with the son's picture on it and one with the info about friends, etc.
So he feeds the second cube to the computer. "It spits it out." He puts the cube in again, so as to make sure he really got
all the information from it--"appetizer" as in:
"something that stimulates a desire for more a literary appetizer hoped that the short trip would be an appetizer for longer ones"
https://www.merriam-webster.com/dictionary/appetizerIt makes sense here; the lady calls the computer an "old broken-down machine." You see, the guy is asking her all these questions she doesn't really want to answer and the only thing she leaves behind is a lot of money and a cube with a bunch of names, telling him before she goes through the door that he shouldn't disappoint her. So he wants to make sure he retrieved everything he could from the cube..