Colour accuracy cannot eyeball. You need to calibrate using a colorimeter.
PC or notebook? What graphics card do you have? If it cannot support 2560 x 1440 at 60Hz, then your HDMI from your graphics card (and also possibly your cable) is less than version 1.3 which is old. Either that or you're trying to run at extended distance.

Suggest you upgrade your graphics card if it's a PC or a new HDMI cable if it does not support version 1.3. A cheap graphics card already can have almost all the necessary connections you want. The time and effort to hunt down for a convertor that MIGHT work sometimes not worth it and probably as expensive as a graphics card itself.
Not possible to have DVI to DP. The world will be upside down if that were possible. 
A quick check before getting a new DP cable would be to try using a different power socket from monitor to the wall or a new power cable? It solved the problem for me when I switched to a different monitor requiring 2 x DPs. Have not checked why but I suspect the power socket on the extension cord I was using was a little faulty. Can happen.

A quick check before getting a new DP cable would be to try using a different power socket from monitor to the wall or a new power cable? It solved the problem for me when I switched to a different monitor requiring 2 x DPs. Have not checked why but I suspect the power socket on the extension cord I was using was a little faulty. Can happen.

or faulty cable

...since it's just fullHD... there's the HDMI alternative...

Hmmm... 4 DP ports? What card is that? 

If there is HDMI on you GC.... you can easily convert HDMI to DVI...