I spent a lot of time researching and learning, so, should I use laptop's Thunderbolt 3 output with (Plugable USB C to DisplayPort Adapter), which was mentioned in this topic above?
HDMI 1.4 , according to what I read, it can offer 144 ghz at 1920x1080?
An HDMI to DisplayPort adapter will not work with FreeSync, no.
The G2590X I think is a good option. The 24.5" panel it uses is a newer panel as well, which supposedly has improved image quality compared to the older panels most 24.0" 144 Hz monitors use. Haven't tested any myself though.