I am a dog trainer in training and also own two dogs. One is two years old and one is eight weeks old. Puppies bite and nip because it's their way of exploring their world because they have no hands. I don't agree with yelping when bitten by a pup because it may have an adverse effect on some pups. The pup might repeat this just to get your attention. What I am finding out right now with my new 'baby' is if you are holding her or him and the pup begins to bite, offer it one of it's chew toys to bite on instead of your hand or fingers. Don't get the pup in the habit of biting you. You can also spray your hands with bitter apple spray and this will help deter the pup because they don't like the taste. You can also train her not to nip by holding a tiny bit of a treat (I use soft liver treats) in one hand and while she's trying to taste it, pet her with the other hand.
Also, don't 'rough house' with your pup or play slap. This only encourages the pup to bite more.
For the begging behavior: A strong 'sit-stay' or 'down-stay' is usually recommended to correct this. The dog should never get treats or any type of food from the table or kitchen counters and never give your dog anything you are eating while you are eating.
The 'leader' of the pack which is you, always eats first, not the dog. You can prepare his food but don't put it down for him until you and your family have started eating. Once you all sit down, someone can get back up and feed the dog. Before you put the dish down, have your dog sit and stay. Put the food bowl down and give the cue, "OKAY"! Go back to eating your meal. If he doesn't start eating it in a minute or so, remove the food bowl. He will learn he had better eat his food or lose the priveledge.
There is no 'free lunch'. A dog should always offer something in return for everything he gets. If you want to pet him, make him sit or lay down. I can tell you this by experience, your dog wants you to be the leader and if you are consistent with your obedience training and remember that training is a life long commitment, you will have a happy dog and one who is well trained. If you don't show your dog that you are the leader of the pack, your dog will take the lead and that is only going to lead to frustration and bad behaviors from your dog. The number one cause of death for dogs is bad behaviors uncorrected. The dogs wind up in the shelters then put to death just because the owner didn't know how to train him properly or didnt want to. Good luck.