I feel for you, because you love the dog and want it to behave so you can enjoy each other. Unfortunately, shelter dogs can come with a lot of baggage. In many cases it's why they're shelter dogs in the first place. You actually know a lot more about this dog than most shelter dog owners know about their dog.
I feel for the dog, because it has had it's whole world torn apart, by the death of the old man and the dog's sibling, both of whom it had known it's whole life, and then being abandoned by the old lady. Shelters are not good for the dog's psyche either, maybe especially so for small dogs. Scary places for sure.
I would venture a guess that the dog is acting out because he is insecure and fearful, perhaps of his new environment or because of a perceived lack of support from his pack. Whatever the reason, it will be hard to change the behavior if you don't know what triggers him.
I would buy him a snug fitting harness or "thunder shirt", and have him wear it anytime he's around other people or animals. Sometimes it's enough to make the dog feel safer. If you walk him, get a pinch collar and keep him leashed. I would advise going for walks every day to train him.
Watch his body language, and listen for verbal clues like growling or barking. If he shows any aggressive behavior a quick sharp "pop" on the leash, combined with a strong and firm NO will let him know what you expect from him.
Don't yell "no", just be strong and firm, and try to keep emotion (anger, panic, anxiety) out of your voice. Your dog will feed off your emotion, probably for the worse. Keeping your voice moderated projects confidence, and being absolutely consistent and fair with the dog will build his confidence as he learns his parameters. Besides, volume does not increase comprehension! Consistency does. Same expectation, same command, same correction. Every time.
I would NOT recommend a shock collar. The dog needs to know the corrections come from you, and the absence of a tether and the kinetics involved may leave your dog not knowing where the correction is coming from. It will only make the dog more afraid and neurotic.
If all else fails, you could have his fangs pulled as a last resort, short of putting him down. Good luck!