I am really sorry you are having so much trouble with your bike. I know I would be totally fustrated also.

When you pedal backwards even when you are just clipping in the chain needs to be pretty much straight from front to back. I was doing the same thing when I first got my clipless pedals as before I didn't have to pedal backwards to start. I would be in the largest sproket in the front and if the chain was in too easy of a gear in the rear, it would fall off. I now usually stop my bike when the rear is in the 3rd sprocket from the top, front is in the largest.

The crank Specialized uses is really made from a larger company and they just put their name on it. You can probably find the name of the company in back of the crank somewhere. The jumping of the chain can actually stem from your derailleur that needs to be adjusted more. I am getting this info from my husband. He says derailleurs are a real pain in all bikes at some point, however, sometimes like in your instance it might take a bit more time. Trek, Cannondale any of the name brands can have a derailleur that may take a bit more patience to get it adjusted correctly.

I will be honest and say that if you do feel the need to get a new bike, I wouldn't blame you if you looked into different brand. Be sure to test ride the one that they are giving you to purchase before actually purchasing it and change those gears real good, all three in the front and all in the rear. Although you probably thought of that already.

I hope I did not come off sounding like a know it all or anything, I just would like to try to help in areas that I can, well with the info really coming from my husband. I wish you luck with whatever decision you make.

JoAnn