OK first - if he is asking to go out in the middle of the night (even by waking up) why are you not taking him out?? He obviously had to go if he ends up going in his crate. We had to take Loki out in the middle of the night until he was at least 1 year old.
Why can't you just buy a carpet steamer? We bought a little bissell for like $60 and we've more than gotten our money's worth. The spot only smells if you don't clean it right! Enzyme cleaners are your friend.
I have 2 that are housetrained. It did take until the were a little older, but they got it! It is possible! (But, guess what, they still have rare accidents. And yes, they both know they are supposed to go outside and they are truly accidents - like they asked to go out and I was busy and they really had to go!)
BUT, even with fully trained dogs - it does not mean your carpets are not in danger. Mine puke on the carpet - steam cleaner! Heck my neighbor borrows our steam cleaner all the time for her LAB when he gets sick. It happens! Her dog ate and puked up a blue bone that is never coming out...
We put wood downstairs and we'll replace the carpet upstairs before we move - but we would have done that anyway!
Oh and yes - if you crate him all day he will be hyper at night. Go for a very, very long walk and make sure he is EMPTY before bed. It helps, really!
There is hope but you really do have to be patient and be willing to tolerate a little mess. If you aren't willing to do that, then you might want to consider finding him a new home now. We got Sammy at 10 months and we love her! Re-homing isn't a bad thing even though it is hard.
Good luck!