Rewards
The basic question here is "why would a dog do what you ask it to"? Especially if that has no relation to what the dog wants. And the answer has to be
either because you reward him for his compliance, or you punish him if he doesn't. Dogs (and people) don't do things just because somebody wants them to (and "because I say so" is not a reason). They do them because there's something in it for them (rewards) or they fear the consequences if they don't (punishments). We on this site feel that the only appropriate way of teaching a dog is via positive reinforcement (the giving and withholding of rewards).
Sooo. You want your dog to come in when you open the door. What does he get for doing so? He's not necessarily whining because
he wanted to come in. It's just as likely that he's whining because he wants
you to come out and play with him - in which case coming inside is the opposite of what he wanted. Try rewarding him for coming in when you ask instead. It will probably make quite a difference.
Same goes for waiting to let you clean his feet. There's nothing in it for the dog unless you provide some sort of reward. And he's most unlikely to be able to understand that his feet are muddy and they need cleaning rather than just being wiped on the carpet and couch

So - you want him to wait to let you clean them: make sure there's something in it for the dog. He needs to be rewarded for compliance with your wishes if you hope that he'll eventually start to offer his feet up for cleaning.