I can download MSYS from MinGW
YOu can.
and it will do everything(I hope?) for me.
It won't. MSys provides environment for building software that requires unix-like environment. To be more precise - autotools. If you aren't familiar with *nix build process (configure script), Mingw won't really help you.
However, from what I see there, it says that MinGW comes with already built version of GCC,
Yes, version 4.7.2 at the moment.
meaning I won't be able to use mine anyway. Am I right?
No. If you don't add Mingw/MSys to your PATH, you can keep multiple different installations on the same machine. It also SHOULD be possible to use multiple different versions of gcc within the same installation of mingw, but things can get messy here. (gcc3 and gcc4 should be able to exist, not sure about 4.7.2 and 4.8.1)
If yes, what should I do to build and use GCC?
You should search for precompiled binaries provided by somebody else. Compiling gcc yourself is possible, but for you (i.e. if you aren't arleady familiar with msys) it might not be worth the effort.
Either you could try http://mingw-w64.sourceforge.net/ or mingw-nuwen. Mingw provided by nuwen is 32bit only, but is very easy to install. The problem is that standard mingw distribution includes update tool (with "mingw uppdate" and "mingw upgrade" you can upgrade installed packages to their latest version), bug "mingw-nuwen" doesn't have such tool.
Because you say
However, I completly have no idea what to do with these lines.
You should either use precompiled mingw provded by somebody else, or use another compiler. If you don't really need bleeding-edge C++11 support ON WINDOWS, use visual studio express.