ok where to start,
first I have a loptop which has only hdmi display port (razer blade)
and I have ASUS VG248QE monitor which supports 144hz

Ive read that hdmi doesnt support 120hz (maybe new versions?) or hdmi to dual-dvi?? I dont care about exporting sound but 120 hz is important. so what should I do, this is problem 1

the secound problem is, I open quake live, and it is 125fps, after like 4-5 seconds it change into 60fps.. its reaaaaally annoying, I have checked and it says that my last renderer is nvidia card(vsync is off) but on my intel 4600 it cannot be disabled (stupid guys). so what should I do? playing with 60fps is pain in the head.

I disabled the integrated card from device maganer and the computer became reaaaly slow, then I re enabled it, now in the game it doesnt matter fullscreen or not, I got 125fps. This is nonsense I know but thats the result.

For 120hz output ill try 1.4a hdmi, if it doesnt work I will try to get a dock as one of the comments, it connects to the computer from usb3.0 and it gives us a lot of connections (jacks, hdmi, vga, dvi, hdmi) is there any one who used it? can I get 120hz with it