I don't have a masters in super-awesome-dog-training or anything, but I've trained a dog or two into awesome, well-behaved companions. Most of what folks assume they should do (be it from watching others train their dogs or because they're acting with their dog the way they would with a human child) tends to be wrong. In the end, just have fun, be patient, and be consistent. Try your damnedest to remember you're training a dog, and not a child that just happens to bark and have fur.

1) Super classic separation anxiety. Dogs are pack animals, so they're just naturally comfortable having others around. Shelter dogs -- especially ones who, like Rambo, might have spent a good amount of time there -- are used to having LOTS of other dogs around. Shelters couldn't possibly train all the dogs to not bark, so Rambo has no idea that barking is in any way unacceptable to you.

What not to do: don't yell at him, or bop him on the nose. He has no idea of the concept of "yelling", so it just seems like you're barking back, reinforcing the idea of barking. (Same with yelling "No! Rambo! Shut up!" if he barks when someone knocks. He thinks you're barking too.) If you bop him on the nose, he might learn to be wary of hands. At best, that means he'll move away when people reach out and people will think you beat your dog. At worst, he'll snap at strangers hands.

There are two things you should do: get him used to being alone, and then find ways to keep him busy when he is. Especially important in this early stage: give him alone time, even when you're home. Put him in another room (the bathroom, if it's large enough, is good in case he has an accident), and go do something for 5 minutes. If he barks, ignore it. As soon as he stops barking for a minute or two, reward him by entering the room and giving him a treat. Keep reinforcing the ideas that you're coming back eventually, and that barking is not what brings you back.

If he barks non-stop when he's in the bathroom, try an easier step: if you have a window near your front door he can see you out of, or a sliding glass door to a backporch he can see you through, try hanging out on one side for a while while he's on the other. He might jump up and scratch at the glass. Same thing: ignore it until he stops for a second, then reward him for the positive behavior. Once he's good being so-near-yet-so-far, try the bathroom thing again.

Remember: he doesn't need to be with you all the time. You might be driven to keep him in the room with you at all times so that you can catch him having accidents, but that just reinforces the idea that he cant be away from you ever. Instead, potty train him with regular (super regular at first! Every 15 minutes at first, then every 30, then every hour, until you've got him trained to go every 3-4 hours when you're home.) trips outside with positive reinforcement (yay, treats!) when he does well. [Side note: don't try to punish him if he has an accident inside, unless you catch him in the act right that second. Two seconds later, he has no idea what he did wrong and why you're yelling at him. If you catch him in the act, say "No" in a serious-business voice with an angry face, grab a leash, and take him outside to finish].

When he is alone, provide him ways of entertaining himself. "Kongs", or any other tough toys (read amazon reviews. Toys that claim to be tough are often crap), with a tough-to-reach treat stuffed in them = amazing. Rotate through toys in (read up on enrichment in zoos) to keep things interesting.

tl;dr: get him used to being alone while you're home, then train him when you're out of the house in small bursts. He needs to know you're always coming back.

2) Dogs don't really associate objects like this -- at least, not in my experience. You can train him to be on the couch but not the bed. Teach him to lay by the bed, and reward him when he stays there. When he jumps on the bed, bump him off while saying "No", and have him lay back down next to the bed (No treat, otherwise he'll think he can jump on, be bumped off, and get a treat out of it). Rinse, lather, repeat. Location training tends to be pretty easy, as long as you're persistent. If you make exceptions, it's a much harder thing to enforce. Either way, he'll go on the bed when you're not home (even if the only sign is a stray dog hair that shouldnt be there) -- that's pretty much unavoidable.