Biting and whining are normal methods that puppies use to communicate and explore the world. While biting and whining are perfectly normal, that doesn't mean you want to put up with those behaviors, either in your puppy or your adult dog. While it will take a little work for your puppy to learn what behavior is appropriate, you may be surprised at how quickly your pup learns the rules of the house.
Teach your puppy bite inhibition. Most puppies are not being aggressive when they bite, this is how they play. Your job then is to teach your puppy that this is not the way you like to play. Any time he bites at you while you are playing, stop moving and say "ow." Don't jerk away, as this sudden motion will seem like part of the fun to your dog. Stay completely still for 10 seconds, then resume playing. If he gets rough again, repeat the process. If he continues to play rough, stop the play session. Repeat this process until he learns how rowdy he's allowed to get during playtime.
Ignore whining in the crate. When your puppy whines in the crate, he is expressing his displeasure about being left alone and wanting some attention. If you keep going back to slip him a treat or tell him everything will be alright, you are rewarding the behavior. Avoid leaving him in the crate for long periods of time, make sure he isn't hungry or thirsty and make sure he has had a chance to use the bathroom. Give him a chew toy, perhaps one stuffed with treats, to keep him occupied. Once you know there is no reason he should be uncomfortable in the crate, leave him there and ignore the whining. He will learn it is a waste of time.
Provide your pup with plenty of exercise. Much of the bad behavior puppies get blamed for is the result of too much energy. Make sure he has the opportunity to chase a ball or go for brisk walks several times a day. If the only time he goes out is to use the bathroom, you shouldn't be surprised that he wants to gnaw on your hand every time you sit down or whines and cries when you stick him in the crate.
Reward good behavior. When your puppy is behaving the way you want him to, reward him. If he is lying quietly in his crate when you walk in the door, toss him a treat and let him out immediately. If he plays a game of tug-of-war without grabbing your hand, reward him with praise and a walk outside. Teach him how you want him to act by rewarding him when he behaves.