Chain stuck between cassette and spokes and damaged rear hub - any way to fix it? My rear derailleur didn't have limit screws properly adjusted so when I shifted to the biggest chainring the chain jumped in between the cassette and spokes.

I managed to get it out but then noticed that the hub wasn't coasting anymore - when I push the bike the pedals are also spinning (just like fixie).

I removed the cassette to check what's wrong and saw that the hub was damaged and now it's rubbing against that moving part where I mount the cassette (don't know how it's called). Is there a way to remove that moving part and smoothen damaged side of the hub? Or I need the new wheel?

Here's the pic of the damage so it's a bit more clear what I'm talking about:



EDIT: As Argenti Apparatus advised I brought the wheel to the bike shop. They assessed it and fixed it - filed the side of the hub so freehub can spin again and replaced 7 spokes.
My wheel wasn't super expensive (Shimano RX31 I think) but repair price was still much cheaper than buying the new wheel.
Also thanks to everyone for your input and teaching me about the freehub!
That's a bit of a mess. Looks like the chain dinged up the hub, freehub body (that the cassette mounts on) and the spokes.

The freehub body is removable, and you could possibly use a fine file to remove any metal burrs that are keeping the freehub from rotating. 

What is far more worrying is the state of the spokes. All the drive side spokes are gouged and at least one is bent. I'd have a bike repair shop look at it to assess the extent of the damage. Best case you can replace a few spokes, worst case all the drive side spokes need replacing, or if the hub is not salvageable you are looking at a new wheel.

Have the bike repair shop adjust your derailleur while you are there.