So far looks like I've fixed the second issue I had. Even I had all sleep/hibernate/turn off hdd/etc settings disabled, I had "4b" and "1" values in registry under HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Power "HiberFileSizePerfect" as "4b" and HibernateEnabled "1". Seems like even I turned hibernate off from power management, it was still set on for some reason. I didn't notice that my computer would have hibernated either because those lines I had in the imgur pic I posted didn't come after same amount of time, but randomly after a longer idle. Never during using my computer.
For the first issue, I more or less have a fix for it right now. I got 60Hz working on with 1280x1024 resolution, even with 75Hz for my TV. Higher ones still blinks.
For 60Hz I got more or less working fix too right now, but colors doesn't really show properly after that (they're way too bright. Even my BenQ G2420HDB shows black as blacker than my 46" Sony HX723 when normally it's the other way around). Went in CCC to "My Digital Flat-Panels" -> "Pixel Format". Setting was YCbCR 4:4:4 Pixel Format. After changing that to YCbCR 4:2:2 Pixel Format my TV stops blinking. If I choose either one of the RGB Pixel Formats, TV starts blinking again.
I'm really wonder if it's just a driver issue with HDMI as some people have said when I've been googling for it. I don't have any miniDP cables/adapters I could test those ports to see if they do the job as they should.
EDIT: After some minutes of using it with YCbCR 4:2:2 Pixel Format my computer forces YCbCR 4:4:4 Pixel Format back. So this thing didn't really work either.