Short version: you need git, and you should follow the instructions in Compile.html as closely as possible to avoid pain and suffering.
Visual Studio isn't necessary however it normally comes with the required C, C++ and C# compiler and libraries. Without a compiler you can't build anything.
You could use Eclipse if you can setup a C++ compiler for your builds
Visual Studio is
absolutely necessary. DFHack is loaded in the same memory space as DF, and must use the same runtime libraries, or it will crash. This means that it must be built with the same compiler as DF, which is Visual Studio 2015. Some people have had luck using the 2015 compiler in VS2017, but I'm not sure of the process there, so I would really recommend VS2015 to make things easy.
If you can get Eclipse working with the VS2015 compiler, then it might work, but otherwise it will not.
and you can go to the GitHub repo and just "download" the master branch as a zip yes.
No, you cannot do that. DFHack contains several other repos as submodules, which will be downloaded if you use git (and follow the instructions in Compile.html), but the "download ZIP" option
will not download any of them, so the build will fail at the configuration stage (in fact, we added checks at the configuration stage to prevent people from doing exactly this).
To be clear, we always appreciate contributions, but things go much more smoothly if you follow the build instructions - they were put together for a reason. We also really prefer that you use GitHub to submit pull requests for things to be added - sending in raw files quickly becomes a nightmare when we make changes after merging but you don't update your copy with those changes, etc.
In case you were unaware, there are two main branches of DFHack that you can get with Git - "master" (stable, most recent stable release) and "develop" (less stable, but with newer changes after the last release). I imagine that the master branch is fine for general plugin development, but if you want to work with 0.44.10, you'll need the develop branch for the time being. There are two corresponding versions of Compile.html - they're usually mostly the same, but it's good to look at the right one:
https://dfhack.readthedocs.io/en/stable/docs/Compile.html (master)
https://dfhack.readthedocs.io/en/latest/docs/Compile.html (develop)
EDIT 2: Okay, I lied. I have no idea what I'm doing. Can somebody explain to me how to build dfhack or whatever? It makes zero sense to me.
If it's a matter of the instructions being unclear, I'd be happy to work with you to improve them, but I'd need a bit more specific feedback. How far have you gotten?