Do I need a derailleur hanger for this?

Hello all,

I want to replace this 7 speed Shimano Altus Rear derailleur on my wife's bike because it is all bent and corroded.

I would like to replace it with this one:

https://www.bike-discount.de/en/shimano-alivio-rd-m3100-9-speed-rear-derailleur?number=20084144-40214272&__delivery=5&__currency=1

1. Do I need some kind of derailleur hanger? Or will it just mount to the frame (green)? I am confused about the black part on the existing derailleur, is that a hanger? Or just part of the derailleur? (if it is a hanger, I'm sure its bent, so what do I replace it with?)

2. I know the Shimano Alivio m3100 is a 9-speed, but I'm told it will work with the 7 speed drivetrain just fine? I'd like to get this one because it looks higher quality than all the Tourney, Altus and Acera ones. Will it be harder to setup being 9 speed vs 7 speed?

Thanks for any guidance!