The mingw folder contains a copy of gdb.
If you have gdb in any other place, you can configure the IDE to use that other gdb. (Tools > Option > Debugger)
There is also a copy of LazGDeBugControl.exe. This is only necessary when debugging cross-bitness. (I.e. 64bit vs 32bit)
If you do cross bitness, and use another gdb, copy this file into the folder where gdb.exe is.
Alternatively you can setup the IDE to use the beta LazDebuggerFp. (search for fpdebug on forum/wiki)
I wish if all these programs are going to utilize mingw that they would either ask you or search for an existing copy on your hard drive instead of numerous copies of the same compiler being installed.
There is no compiler in that folder.
Only gdb.
At least on Windows:There are a few mingw tools in the fpc folder. (eg make and ld)
And I advice to keep them.
Fpc may work with other versions, but it could also fail.
No one will be able to solve any strange errors that you get by having another toolchain in your PATH.
And again its not the entire mingw. Only selected files, that take not very much space.
There is a copy of gcc. That is only required for compiling resources (which I think includes lfm files). Its required by windres.exe.
But again it probably needs to be kept.
But well you can try to include them from elsewhere. Until eventually you get mysterious errors. Or if you are lucky it may work....