Is this normal for my dog?

These are all things that can be corrected with training. Training isn't just for showing off, training also gives your dog confidence, which in turn will help it with things like separation anxiety. You shouldn't let your dog be like this, as it will only get worse. Some dogs get so scared that they actually turn aggressive, lashing out at everything because they are afraid of it. You should contact local dog trainers and see what kind of classes they offer, or ask your veterinarian for recommendations.