I only got that far after switching over to MSYS2 as per the instructions. I'm not entirely sure WHAT MSYS2 is, other than a Linux command line, so I'm not entirely sure why it is needed over Window's command line.
Ah, so it's a shell. The last time I used a windows command-line was in the age of Win95 or so, but that commandline is not even comparable with any Unix shell. A shell is a powerful and complete programming language with variables and text substitution. It's not only used for interactive typing commands, but also eg 'make' runs its commands through it, ./configure uses it, etc. It's sort of a scripting layer on top of the plain commands that acts as glue. Many tools willl fail to work without a shell.
The "mpfr-3.1.2-2-mingw32-src.tar.lzma" archive didn't contain any source code, at least not at first glance. For some odd reason, that archive includes another archive with the actual source and a "package.ini" file that unpacks it. This isn't mentioned in the instructions, nor why such a thing would be needed.
The normal procedure is indeed to pull a real source file straight from the Internet, unpack, and build. Apparently the "mingw-get source mingw32-gmp" did some additional stuff (at least now it does). You may want to read what "mingw-get" is doing, under the assumption it's trying to help you. The Internet may be helpful, if you have man-pages installed (and the command has a man-page), "man mingw-get" should give you help too. Note this is generally reference documentation, rather than a tutorial.
There are THREE makefiles, MakeFile (no extension), MakeFile.am and MakeFile.in
Ah, ok, so it's likely an automake project. The Makefile.am files are the real source in that case (unless there is another code generation layer I am not aware of). GNU automake has extensive documentation that you may want to consult.
automake generates an autoconf project, with configure.in (or configure.ac depending on age of the tool) and Makefile.in files. autoconf uses configure.in as input file, and generates the ./configure program. When you run that, it knows what to look for (C compiler, blah library, blup command, etc), and uses the other *.in files (eg Makefile.in) as template for generating the same file but without .in extension, and with the found system information, like GCC=/usr/bin/gcc.
That gives you the Makefile that you can use for "make".
GNU also has documentation for autoconf, libtool (very smart library build program), and conventions in these generated Makefiles with usable targets, and other things for makeing a real GNU program. In case you want to know, look for something like "developing software with GNU" or so.
Understand that this library is the easiest of the ones I've tried. GTK+ and Cairo are lost causes.
That sounds about right, although I have no idea how portable any of these libraries are (or supposed to be).
What I really need is a tutorial that will teach me how to port over Linux projects to Windows, with details on the structure of MakeFiles, command line everything, what to include in the projects, how to determine, etc. Whatever I would need to do this for any project I find. I cannot find such information.
No idea about porting guides, my guess is that very few people actually do this. Makefiles and a lot of other stuff are very well documented by GNU documentation https://www.gnu.org/doc/doc.html is the entry page. Note that "the GNU way" of doing things is just one way. While it likely provides you with a lot of context not all projects are run this way. GNU coding standards https://www.gnu.org/prep/standards/ seems a lot more than just coding standard, maybe useful to browse that too.
Edit: I missed "command line everything". GNU has a Bash manual, I saw, that should help (shell as programming language), otherwise, "unix shell commands" or "unix command line" or so likely give you a zillion Internet pages explaining commonly used commands. O'Reilly used to have a number of books for it too, no idea if you can still obtain them. Further up in complex commands, Linux Powertools comes to mind, not something you'll immediately want, I think.
It would seems that the assumption is that anyone wanting to use these libraries or any GNU library already knows how and they make NO allowance for Windows developers.
I think this is normal, Windows or Apple isn't much better, except it happens to be the system you grew up with, so you had a life-time of studying to learn what you now assume is general knowledge for all :)
Hope this helps.