Ditto on the obedience classes and perhaps a behaviourist to observe you.
I do see where you might indeed be confusing him. You push him off your bed yet you sit on the floor with him. First off, let's get the safety aspect straight. You say he has bitten your face. So DO NOT put your face where he can bite it, get up off the floor. Second off, elevating yourself (or lowering him off the bed) is a technique you can use to enhance your authority but you ruin it when you sit on the floor. I bet this does confuse him. I bet your Dad does not sit on the floor with him. Right?
Marking. Neutered dogs mark too. Maybe his former owner was one of those poor deluded souls that think neutering is a magic bullet and didn't stop him marking when he started. Once they learn to mark neutering might stop it but it might not. No guarantee. You have control on walks, simply decide when and where he can mark and make him walk properly the rest of the time. I do feel it's only fair to allow some time and place for dogs to check their peemail though.
His behaviour with guests is totally up to you; leash him. An obedience teacher can give you many tips on how to train him to be polite with guests, till he is, leash him.
The possible breed mixes you mention are all working dogs that benefit from exercise AND mental stimulation. Most dogs do, really. An obedience class can help there and you might find he has talents that would suggest a competitive venue, like agility or maybe just more obedience. You don't have to actually compete but many dogs enjoy the training.
The change in behaviour with other dogs is the most concerning, I think, and I would Vet him to see if something is off. Thyroid comes to mind as it can sometimes seem a dog is aggressive when it never was before. It might be stress from the move but it would be good to rule out a co-incidental medical problem.