Ok, so several things...
1. This is exactly why it is recommended to keep a new kitten in a "saferoom" for a while, until you are sure that they are confident in their surroundings, with the house's inhabitants, and is good with his food and litterbox. And that is advice for a 13 week old kitten that has been raised in a quality cattery sort of situation!
2. For your cat this ought to be especially true, given the kitten's tough upbringing that you described. He really really really needs a saferoom where is world his relatively small and manageable for awhile. At his age, you might actually have to do that for a few weeks or even more. Really bad idea to just open his cage and give him the run of the house!
My advice is: put him in a single room, have at least one litterbox in there, maybe more. Have his food, toys, something to climb on, and visit him frequently. Play with him, feed him, comfort him, let him know that he is loved, but don't overwhelm him. His world needs to be that small room for awhile. When he's doing really really well, with rock solid eating habits, litterbox habits, confidence with his surroundings and people, then THAT is the time to give him more.
_________________ The little monsters 3
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