When your keet shakes, does his feathers ruffle? If he is ruffling his feathers, he can very well be cold
Is he in front of a window or by a vent? Try moving his cage out of the way of drafts if he is. When birds ruffle their feathers its to conserve heat. It can mean they are cold, or can mean they are sick also.
If he is not ruffling, just shaking then he is probably scared. For now, you might want to leave him in a low traffic room. Where he will see you enough but not so much that he stresses out. I advise to keep the puppy out of the room for the first week or so, so he can get used to his new cage, home, smells, feeding time etc. He's going through a stressful time, and every little thing can help
Is his cage against a wall? Most birds feel a bit more safe with the back side of their cage against a wall. Just so they can feel their back is protected.
Will he continue to bite you? Maybe. All animals have the instinct to bite, and can very much do so. Is he doing it because hes mean? Of course not, hes doing it because he is frightened. Do not hold him at all for the first week he is home. He needs to get used to everything else around him. Then you want to introduce your hand into *his* territory, and offer him some fresh fruits or veggies from your fingers and gently stroke him if you can. Eventually work on having him step up. If he wildly flies around his cage, don't try to work with him just simply shut his cage and try later.
I hope this helps you, and good luck with your new fid
They are such a joy! Pictures would rock