Be careful when allowing your child to run when a large puppy is around. Puppies love to chase, and they may nip when they catch up. This is not aggression on the part of the dog, it's just the way puppies play with each other. They roll around and nip each other, working out who is dominant. This behavior will eventually stop when the puppy reaches adulthood.
Puppies love to play.
And adult dogs who were lonely strays on the streets are so happy to have a safe and loving home, that they're bound to be playful for a while. They've certainly had no opportunity to play out on the streets. It doesn't take a lot of effort to play with your dog and make him happy. I play with Binks even when I'm watching television. She brings her tug rope or stuffed toy to me, and I pull on it with her and throw it.