Busted my bike hub & derailleur (I think) - how bad is it? I screwed up :( Background leading to my foolishness: I've been straining my bike quite a bit with hills and inclimate weather, and I haven't been able to find my maintenance kit since I've moved, so in my busyness I've let myself push around on a squeaky rusting chain. I realize I may be learning an expensive lesson now.

Today I kicked off and start pedaling, finding my chain was jammed up and not moving smoothly through a full rotation. That has happened before with a poorly oiled chain and I've pushed or shifted my way back into relatively-smooth operation. Well I pushed and it was stuck, not moving forward at all. Should've got off there but instead I pedaled backward a little, shifted and pushed, and it moved a little. That inspired me to push harder, and in my haste I pushed recklessly hard to pedal forward. Well, it stayed stuck and felt pretty wonky at that point, so I calmed down my haste and got off to check what's wrong. I found the back wheel had tilt/camber to it and the derailleur was bent out of alignment - I was definitely not getting anywhere quick anymore! 

I'll bring this to a local bikeshop ASAP to get repaired. Seeing what appears to be a weld severed, I'm not sure if this is a costly repair or a major overhaul I'm looking at. How bad are the damages, can you identify what specifically appears damaged and in need of repair? Is the frame and hub okay to keep and just needs a new derailleur?







From a different angle:





Rear wheel appears normal to me, no clear damage on axle, spokes, wheel frame or anything. I think the connection point for the rear wheel to the frame is what got busted in some way from my pushing, which led to the derailleur getting bent and the wheel off-camber.
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.