A monitor would be compatible with a video card if:
1) The screen resolution is less than or equal to the video card's maximum screen resolution
2) The same interface is accepted (VGA, DVI-D, DVI-I, HDMI, DP, etc.) (This can be manipulated with adapters like HDMI to VGA, or DVI to DP)
That's it for normal monitors. Now if you want to make use of DFRC (Dynamic frame rate control) features, like FreeSync or G-Sync, you would just have to make sure both the monitor and the video card have that feature.
For Adaptive Vsync, I'd really only suggest using 1 monitor at a time for it to work properly. Otherwise you may get a lot of screen tearing anyway. If frames are refreshed faster than 60hz, then you'd be locking your 144hz monitor at 60hz, thus making it pointless to have such a beastly refresh rate. If frames are lower than 60hz, you may get some Judder as the video buffer isn't receiving new images to display fast enough to keep up to 60hz. Other people may attest to using VSync on dual monitors, or you can search the forums for more info on it. There is lots of info out there.