SRAM call this 'HRR'.
Old parts, but 22 speed is new enough. Check that if you buy they are not subject to a recall.
To undo the bolt attaching the brake mechanism to the fork, you need a Torx 25 star-shaped bit.
I had one in my toolbox, but they are readily available at DIY shops - just google ‘torx 25 bit’
There are two bolts on the brake mech, but it is only the bottom bolt which screws into the shoulder/boss on the fork, I didn’t touch the top bolt.
Removing the bolt ...
The threaded ports on Magura brakes I have worked on are bigger in diameter than Shimano, so the bucket tool in your picture would not fit, don't waste money on one uneccesarily, though you can get kits like that to suit a whole range of different brakes.
However, Magura have a feature called "Easy Bleed Technology" where you only need to put a ...