Yes, this will happen to any pet that was very close to the family member that passed. Dogs and cats are some of the worst that will be upset. Dogs will try to to the same place where they always met the person. The animal will eventually hopefully get over it.
Absolutely. It is grieving, confused, lost, sad, maybe even angry. It may also feel ashamed. Tell the dog, and really mean it, that you understand it has a hurting spirit. Be kind to it, and help it adjust. Sorry for your loss.