For the crate behaviour, you are doing the right thing, but having to wait up to 30 minutes for him to calm down means that he does not understand what you are expecting, so start small, and reward fast.
Because of his age and lack of training and human interaction before coming to you, he is still just learning that his behaviour has consequences, and that he can control his environment by choosing certain behaviours. This is a big hurdle for some dogs that have been neglected to overcome, but you will see that once he "gets" it, the learning will really speed up.
So asking him to be calm and sitting is asking too much at this time. You want to help him make the connection, but after 20 to 30 minutes of being hyper and wild in his crate, waiting to be let out, he does not know WHICH of all his behaviours made the crate thing happen.
So for now, start small, and be fast to react: approach his crate and click the door open, but hold it closed. Don't say a word, watch him and wait. Not sure what he does in his crate, but wait him out. He will spin? throw himself at the door? try and jump around? Bark and whine? He thinks that one of these behaviours will get the door to open, and will keep trying different things. He has at some point made that association. After a few minutes (should NOT be 20 to 30 minutes, watch him closely), he will stop for a SECOND to look at you, wondering why you are not opening the door. His thinking and reaction is something along the lines: "Hey DUMMY!!! I'm doing MY part of the routine, going nuts here, why are you not doing yours and let me out?"
The Split-Second he stops, hesitates, looks at you, open the door quickly, calmly, and walk away. Not big deal. Next few times you do this, you will notice that he will be checking in with you sooner and sooner, the excited behaviour routine getting shorter and shorter.
When he gets that you approach the crate, click it open and wait, and he maybe give one bark and spins once then looks at you, ask him to sit - be QUICK to open the door and let him out. He might start offering you a sit on his own in a little while after this. If not, but he responds solidly, try asking him to sit as you approach, before you click the door open. Re-inforce the sit with quiet praise as you open the door, don't let him shoot out. Open the crate door one inch, praise and release him as you open the door to let him out. Next time, two inches, etc . .
Yes, no shortcuts, but if you are consistent and work in increments, scary how fast they learn. Using the above technique, I completely extinguished crate spinning in only one week with Gryffon when he was about that age. Never has been an issues since then.
For the back stairs, have you tried throwing treats down the stairs for him when he goes outside?
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Keeta BH, OB1, TR1, AD
Rottweiler/Hairy Dog mix?? 2004-2015