Okay, I'm going to interject here.
I can't speak to crate training. I've never used it and don't anticipate using it. I'm a bit claustrophobic myself, and, perhaps erroneously, don't really like the idea of confining a large dog in a small space - seems a bit like prison, and nothing comes out of prison "kinder and gentler."
That said, anyone I've ever listened to regarding crate training has been adamant that the crate not be used as punishment.
I think, from your descriptions of Alyusha, that you've gotten the Rottie puppy that experienced Rottie owners dream about. He's intelligent and determined and very, very confident. You've probably really hit the jackpot with this one. That, along with getting him so young, is also why you're having this new problem.
The fact that he is very receptive to obedience commands at this age is very good and it tells me that he wants to be a good dog. But he's also challenging you for leadership, and you just cannot let him win this one. You can't win by locking him up. You've got to teach him that you are alpha, but it's got to be in a way a dog understands. When you send him to his cage for punishment, he's going to be in there brooding to himself and it's not going to lead him to acknowledge you as alpha, he's just going to keep trying to take what he considers to be his "rightful" place. Think about the behaviours dogs use to establish dominance and show submission. When you want him to give up his belly in submission, put your hands on his shoulders and gently, but firmly, make him lie down and roll him over. Make him lay that way for a few seconds; hold him down gently with your hand on his chest, then accept the behaviour by rubbing his belly and telling him he's your good dog and make him feel very, very loved.
I really do know what I'm talking about on this one. The dogs I deal with are not only extremely large, they have been bred for centuries to think independently, have no innate submissiveness to humans and to use their own judgement about situations, without having to wait for commands. They are capable of hunting and killing wild boar and the jaguar, as was necessary on the fazendas in Brazil to protect the herds of cattle. Establishing leadership in a way that does not involve physical confrontation is imperative - as it is with a puppy like your Alyusha.
Personally, on this one, I'd just put the cage in the garage and forget about it. The best thing for Alyusha is going to be as much contact with you as possible. And keep up the wonderful work with the obedience exercises. Later on, you and Alyusha might even want to learn an activity, like carting, which is one of the tasks that the Rottweiller originally excelled at many, many generations past.
You're really going to have to approach Alyusha differently; he sounds like he's going to be that extra-special Rottie who's supremely confident - even for a Rottweiller!
Let us know how things progress, please.