Yes. Most puppies do very well around other pets. We would caution to keep your new puppy away from public places where many dogs may be to help protect against any virus or disease. Best to wait till puppy is around 6 months of age. This will protect puppy from all sorts of issues.
Most puppies will bite and chew on things. Please understand that most puppies are only playing when they bite at you. There are times when a puppy will bite to protect itself if it feels scared or overwhelmed.