It sounds like your pup is doing great!
You're off to a really good start with what you've taught him so far, but ohhhh, there is still soooo much to teach your little guy!!

You're just getting started! I would suggest the next thing you start working on would be his recall. Maybe the most important thing a dog can have is a really good recall. Start asking your boy to "come" - but only ask him when you KNOW FOR SURE he's already heading in your direction, and coming right toward you, and say it in a really happy voice!! That way, he'll be successful, and be sure to reward him really heavily once he does come to you!! Then release him right away to go off and have fun again. Practice that as much as you can, on and off, constantly. Having a good recall may be the most important thing your pup will learn - it's one of those things that could literally save his life one day. Don't get impatient with him if/when he doesn't 'come' - it takes a long time to develop a good recall. That's why, for a long time, you'll only use a word like "come" or "here" when he's on his way to you anyway -- that way, when you say "come" (and he's already heading there), he'll go straight to you, and when you practice it that way (a zillion times) it becomes habit.
Oh yeah, when people say "come", I go straight to them. 
It takes lots and lots of practice and time tho - so please be patient.
As for his mouthing/biting, yep, he's a puppy and he'll outgrow that. I would like to suggest that instead of telling him "no" and tapping him, that you grab a chew toy, one of his ropes, a rawhide, or something he CAN chew on (instead of your hand, or your daughter's hand, or a foot, or a shoe, or anything inappropriate, for that matter), and quickly stuff it in his mouth. He'll quickly get the idea that
oh, that's what he's supposed to be chewing on! Also, and not sure that you're doing this, but don't play the roughhouse games with your hand and his mouth. Many people make that mistake - they play with their hands with the dog's mouth, then later when the dog starts to bite at their hands, they don't like it and can't figure out how to stop it. It's very confusing to the dog. Again - you many not be doing this, so am just saying this just in case. When he does mouth your daughter, tell her to just withdraw her attention from him, turn her back on him - and if she's able, she also can quickly learn to go grab one of his toys and give it to him. No biting hands tho. Please tho, no "tapping him" - he should know that hands always mean loving and pets. You don't want him ever wondering if hands will mean anything unpleasant, and ever become scared of human hands.
You said you don't have a clicker, but clapping your hands and snapping your fingers elicits a response. I'm not sure you understand what a clicker is for. It lets your dog know the instant he does a behavior you're asking for, and is followed immediately by a treat. There are plenty of videos on this site, or Youtube which show what clicker training is, and how it's done. If you're interested in hearing more, let us know and we'll be happy to help you. It really makes training go quite quickly, and training is done using positive reinforcement only - meaning no punishment, no "No!'s", no 'tapping' your dog, etc. Using positive reinforcement and clicker training, you redirect your dog, you ignore behavior you don't like, and reinforce and reward behavior you do like. You end up with a dog who loves to work, looks forward to working and training, and who actually 'thinks' (rather than only does what it's told, but is afraid to do other things, cuz it might be punished if it does the wrong thing). Please let us know if you'd like help, and we'll give you lots of information, videos, etc.