Busted my bike hub & derailleur (I think) - how bad is it?
Updated based on your edits and comments.

The severed piece of metal circled in the 3rd image is one of the cage plates, and was originally attached to the lower (idler) pulley bolt.  Beyond replacing the derailleur, there is no additional damage there.  It really does appear that you may only need to replace your derailleur (and chain).

Other items to check out, at least to verify that nothing else is broken:


If you can spin the wheel and it rotates cleanly on the axle and is straight and the spokes are unbroken, straight, and under even tension then the wheel is good. (If some of the spokes are deeply scored you may want to replace them anyway.)
If the freewheel spins cleanly, and there are no bent teeth or wobble then it is okay.  (Though if you're replacing the chain it may need replacing anyway depending on wear.)  Based on the way the derailleur bent it's not likely it damaged the freewheel, but it's still worth checking.
If the frame itself is not bent (the distance between the dropouts hasn't changed, they are still evenly vertical and level with one another, and the stays are all straight) then it's fine.  (If it's a steel bike then a small amount of bending is survivable, but if it's aluminium it's trash.)
Obviously the derailleur is trash, but the derailleur hanger might be too.  (It's hard to tell from looking at the back side like this.)  You'll probably want the shop to make sure it's not twisted, which would cause the derailleur to mis-align.
You need a new chain, no question, since it sounds like a jammed link is part of the sequence that caused this.