You don't say how long you've had him, which would in part determine how I'd handle the situation. I think you are wise in not putting yourself and your dog in a situation where he might bite you, it's better for both of you that that day never comes.
I'd train with him as much as I could, to establish a rapport with him, gain his trust, and make him used to listening to you, and that this has its benefits, either in the form of treats (SMALL) or lots of praise in an excited, high voice (as opposed to a deep, firm one when you correct him).
I'd try to get him used to you touching his neck, because it's an exposed area that strangers may inadvertently reach for, which could get ugly. When you pet him, maybe work your way to his neck, praise him, don't make a big deal about it.
When it comes to lying on your stuff like that, I'd get him off it first. Call him over to you for a quick pat, a treat or make him sit. THEN get your stuff.
Have his hearing checked - if he's older, and hard of hearing, a sudden hand on the neck might spook him, particularly if he's sleeping or he can't see you coming.
I'd also - and perhaps first and foremost - consult a professional, whether a trainer, the shelter where you got him, a Boxer rescue center, or a vet, to see if they have suggestions or insights.
Good luck and good job! -c