No the monitor does not have speakers. They would be junk if it did so buy a decent set or use headphones.
No, this will not max all games (mmo's yes, things like bf4 or crysis 3, no) at 60fps. The GPU is simply not powerful enough for those high end intensive games. Even with overclocking it will not max games. It will run everything on high though. MMO's should be able to run at max.
You do not need a cPU cooler if you aren't overclocking. The stock cooler is perfectly fine.
Ok thanks a lot! As long as I'm able to play mmorpgs like TERA at 60 fps constant on max settings then its all good to me. I'm gonna go ahead and order it I guess unless someone has any suggestions to make it better, etc.