“Down” can be taught very similarly to “sit.” You can wait for your dog to lie down (beginning in a boring, small room such as a bathroom can help) and capture the behavior by reinforcing your dog with a treat when he lies down, giving him his release cue to stand back up (and encouragement with a lure if needed) and then waiting for him to lie down again. When he is quickly lying down after standing up, you can begin saying “down” right before he does so.
Puppies develop very quickly during their first three months, particularly after their eyes and ears open and they are no longer completely dependent on their mother. Their coordination and strength improve, they spar with their littermates, and begin to explore the world outside the nest. They play wrestling, chase, dominance, and tug-of-war games.
Bring your puppy to the crate for naps and quiet-time breaks so that he can “unwind” from family chaos. Start in increments of 10 minutes and work up to longer periods. Offer treats when he goes inside, and distraction toys, like a stuffed KONG. For years, this author has been giving her Yorkie a treat every day as soon as he goes into his crate and sits. Now as an adult dog, he runs to his crate each morning in anticipation of the goodie.
Submissive urination is a normal way for your puppy to demonstrate submissive behavior. Even a dog that is otherwise housetrained may leave dribbles and puddles of urine at your feet when greeting you. Excitement urination with a puppy is usually caused by lack of bladder control. The puppy is not aware that he is urinating; he's just excited and any punishment will only confuse him.