Hi, it is good that you wrote so much and in detail about your problem.

Here are a few things that i think might help.

When you catch your dog doing something he is not allowed to do, it only makes sense to tell him that immediately (2 seconds is the limit), otherwise he will not be able to connect it with his action. Holding or pressing his nose into his pee will not help at all i think. So whenever you catch him in the act, show him that he was bad and then leave him. So he can learn that this particular action was not one you like him to do.
If you want him to stay in his crate, make it interesting for him. Work with him with the crate, give him some treats into the crate, maybe his favourite toy, anything that he likes very much.
Maybe you can arrange to walk him for a longer period before you leave the house and leave him alone. If he gets the opportunity to drain his energy (and terriers certainly heve a lot of energy usually!) before he is left alone, he might not be interested in walking or jumping around in the house. Especially, if something interesting is inside the crate.
Play with him before you leave, make him tired a little bit, so he is happy to take a rest when you are leaving.
Make your leaving and coming home as "unspectacular" as possible so it won't be anything big for your dog. If you leave, just leave, don't talk to him or stroke him, the same procedure when you come back home: don't watch him or talk to him. Come home, do everything you usually do after arriving, and then, after that, say hello to him. But don't praise him, because he doesn't know what he is praised for (remember the 2 second limit).
I hope i could be of any help and i wish you all the best for the future.
If you have any further questions, just ask.
Best wishes from Vienne
Michael