There is no pack hierarchy, you are humans, your dog is a dog, no wolves, no pack. Just people and dogs living together. These excerices will not change how obedient your dog is or how well behaved he is in other contexts, they will simply teach him a few words (sit and down), something easily accomplished in many ways. Manipulating your dog's physical position will not change how he sees you socially or affect his overall behavior with you.
I would not train these commands with molding (or as they said "modeling") as I feel dogs learn slower this way. They don't have to think about what they are doing, you do it for them. When you ask them to think about their behavior, try and figure out what you want them to do, then they really have to think about their position and it sinks in much faster and more permanantly. Plus since there are no rewards in this particular method it will likely become confrontational. The dog doesn't want to down right now, you make him, he tries to get up, you hold him down, he struggles, you struggle=confrontation, very unpleasant for both of you. It's much easier to just teach him to want to lie down when you ask, this means rewarding him for being in the down position. You can lure, capture, or shape with a reward so that asking for a down isn't a threat of "do it or I'll make you do it against your will" but an invitation of "do it and I'll make it worth your while". Molding isn't always the worst thing ever but without a reward it's almost bound to become a struggle between you and your dog at some point.
What I DO suggest you do is teach your dog to be okay with handling in a positive manner. You said your dog nips when you try these things so it would be good to teach him being handled is good, not mean/restrictive/unpleasant, etc. Start with as much touching as you can WITHOUT biting. If that means one stroke then start there, if that means lifting a paw, start there. Use treats to reward each time you touch or hold a part of his body and he doesn't try to bite. Lift a paw, reward, repeat. Lift and restrict the paw, reward, repeat. Life paw and splay toes, reward, repeat, etc. taking it slow so he never feels the need to bite. If he bites go slower, back up to the last step he didn't bite at and work there for longer. Slowly work up to the point where you can hold him belly up and examine his toes, ears, teeth, etc without protest. This will take lots of time but it will make life for you, your vet, and any potential groomers much easier. Keep these handling sessions SHORT and try to do them when he's not over the top with energy, especially at first.