If so, to what degree were dogs (or other pets) considered family? Could they inherit land? If a king's family died, leaving only their pet, was it possible for them to inherit the throne?
While many people doted on and kept pets I am unaware of any that were given human type of rights like property or inheritance. The attitudes towards dogs and animals varied amongst people. Some considered them just working animals (herding, hunting etc) and others spoiled their pets much like you see today. Dogs and cats were most common but birds and squirrels were also popular. Accessories like collars, leashes and squirrel clothes could be extravagant. Most of my books are in storage but Medieval Pets by Walker-Meikle is a good place to start.