I COMPLETELY understand your frustration. We had LOTS of issues with Emma, including potty training, screaming, and separation anxiety. The good news is, there is a light at the end of the tunnel! It was strange, once she hit the 12-14 week age, all of the sudden she "got it"! She is now 95% potty trained (pee pads for both #1 & #2), she will sleep through the night most of the time, and has learned to be quiet most of the time when she's home alone.
She staying in an x-pen during the day-my husband and I both work 8-5, but I come home at lunch and let her out to play and snuggle for an hour. Her pen has her pee pad, bed, blanket, toys, and water in it, and she feels safe in there. She actually freaks if we leave and DON'T put her in the pen.
We also turn on Baby Beethoven CD's on repeat for her most the time when we leave. I got the idea from a friend who used them on her dog during thunderstorms. Now, when we turn it on, it's her cue that it's time for "Bye-Bye", and she understands we'll be back. You might try this at night-who knows, it COULD work, and it's actually soothing to adults too
Another idea-Emma used to climb on the crate too and we realized she could get out, so we took it out of the pen. (She was never successful though) You might try putting an old bedsheet over the top and some sides of the pen so it becomes a little den for her (make sure she can still see out), and maybe she'll settle and sleep in there. You might need to tie it down for awhile until she gets used to it.
As far as potty training at night-have you tried putting a pad in there with her that she's already "gone" on once or twice? Emma used to get confused when she'd wake in the middle of the night, and stagger off to pee wherever. Once we left the pad that already "smelled" in there, she was much better about using it.
Hope some of these ideas help with your difficult one. I promise you she'll outgrow this and move onto bigger, more mischevious things