
I've not read all your post but what stands out, for me, is the noise your poor puppy is making in his crate. Listening to that noise for 3 1/4 hours would drive me nuts, let alone your neighbour! That's not how to get a puppy to be happy in a crate. You need to set it up in the main room you use during the daytime, leaving the door open and top and sides covered so it's a nice den. With any luck (unless your puppy is now too traumatised re being in a crate) the pup should use the crate as a bed, like any other dog bed. When you need to get other things done (and who can be there 24/7!) play with the puppy so he's a bit tired, take him outside to empty and back to his crate for a few puppy treats and shut the door. If you have timed it right, he should maybe complain a bit but then settle down for another nap. Which is when you do other things.
As for the other barking before 7 am. I'd suggest the neighbour is again quite entitled to be miffed at being woken up by your dog yapping. That too early. Can't you take that dog off to attend to biz if you have to leave early.
As for leaving the puppy crated, when presumably it too makes a noise when you leave - maybe your accommodation isn't going to make any attached neighbour happy.
ps Years ago now we had attached neighbours who both worked full time. They wanted a Westie but were turned down by Westie Rescue - did they take the hint? Not a bit of it. They went up to Scotland and bought a puppy Westie from a man off a ferry. When she came home with them, of course she sounded off when being left on her own. In the end, rather than listen to her, I offered to take her with my lot (in our puppy pen) in during the day, feed her lunch etc. Eventually I decided I wasn't really doing her any favours so she went back. She was quieter. Then they bought a Lab. AND MOVED!!!