Does MinGW support MMX, 3DNow!, etceteras?
It does, well, in fact it's GAS (GNU Assembler) the one that supports them which is the last program called by GCC in the compilation phase.
If you want to add inline assembly to your programs using MinGW you must have in mind things are a bit different. By default it uses AT&T assembly, even though it can be switched to Intel assembly with -masm=intel, but the way to use it is different to that found in Visual C++, Borland C++, Intel C++, ...
Try searching "GCC inline assembly" in Google. There's a nice one around but it's in Spanish.
Dev C++ deos not support any instruction sets
How could it? It's just an editor. MinGW or Cygwin + Dev-C++ is what makes it an IDE, and they both support them.
MinGW, well, GCC, has flags for mmx, sse, ... and processor specific ones.