Ok, compacts can be finicky. However, it sounds like someone wasn't paying attention when they built your bike. The cable should NOT snap off right away. The other end shouldn't unravel with the cap on or for being clamped tightly, even if it does hit your shoe. It was probably already starting to fray from shoddy installation. Then even if your front derailleur isn't tuned properly (which can be hard to do on a compact...that's why I taught myself to do it...my shops kept failing), it should not destroy the rear end of your drivetrain!

I agree with ridebikeme, though I would say that approaching a hill, I tend to shift to a smaller cog or two in the rear if I'm near the inside of the cassette, because chain drop to the inside seems to be more common with compacts, even with the lower limit set properly. By being a little farther out on the cassette, you're less likely to drop it to the inside, in my experience.

This takes some planning, because you don't want to shift harder once you're already on the hill. It took some practice to get a method that seems to make my bike happy. You might find another technique that works once this thing gets fixed.

Now you might want to go over the Performance people's heads and call Fuji. I know they do good warranty service on cracked frames and such. You might be able to get a replacement bike directly from them without messing with Performance. However, since it is just your components, I would first find out where the thing was built. Was it mostly assembled by Fuji or by Performance?