Jesse,

Firstly, if you're not pretty comfortable in Linux to compile and set up all the dependencies, I would recommend skipping the Mac step and running on Linux using the Docker image. Docker relieves you of having to do any of that, but the Docker image is x86/x64 and won't run on Apple Silicon (ARM).  If your final production environment is Linux, your easiest route would be Docker on Linux.

For your more specific questions:
1) yes, those are the links to the ANTs and Niftyreg projects. 
2) On NITRC, our "default" version is Linux native (without Docker). The "Docker" version should run on any x86/x64 but Linux is the only thing we've tested. I'm not aware of anyone running it on Windows. The mac version (native) will run on Mac.
3) Yes, both of those projects use CMake to build
4) In an ideal case cmake builds look something like--
cd folder/with/source/code # folder will contain CMakeLists.txt
mkdir build
cd build
cmake ..
make
sudo make install

and repeat for ANTs.

5) The distribution shouldn't really make a difference. Ubuntu should be fine and if it wasn't working on Ubuntu I'm sure someone would have reported it by now, but we are running Rocky Linux 8 (descends from Centos, which descends from Redhat).

6) Use the included run_mri_reface.sh script

Good luck!
Chris Schwarz