Both of the monitors that you're torn between are going to be great. Both monitors are pretty much on par with each other apart from a few things, something you already know. The Samsung has a refresh rate of up to 120Hz, and the ASUS, with 144Hz.
For everything I've read on the ASUS, the 144Hz isn't really noticeably better than 120Hz - so if you were going to use this as the selling point, you might want to hold on. Even if 144Hz was something that was noticeable, you would require the frame rate to notice it - thus, you'd need to be pushing 144 frames per second in order to justify the 144Hz monitor.
I don't think you'll see this, and I don't recommend the ASUS over the Samsung.
Samsung's S27A950D - which is the monitor I'm looking at while I reply to your question - is an excellent monitor. One of the more standout features over ASUS' VG278HE, is that the S27A950D has DisplayPort. Your video card has a DP connector, so this is something that is useful to you.
Sure, there's no difference to you whether you use dual-link DVI or DisplayPort, but it's there, just in case. You might want to upgrade and buy a second, or third 120Hz-capable monitor, and you'll need DisplayPort for that.
As for your breakdown in questions:
1.) If you are after picture and color quality, you might want to look at IPS-based panels, Samsung make a few and so do Dell.
2.) You'll need to use the dual-link DVI connector, or if you go for the S27A950D, you could use DisplayPort.
3.) This depends on the content you're playing - movies and TV are filmed and played back at 24 FPS, but games - if you're able to reach 120 FPS - will look absolutely amazing (in terms of fluidity) compared to 60Hz.
4.) I wouldn't bother with 3D gaming if you're not going to jump right into it. In my opinion, NVIDIA's 3D Vision is a superior technology because of the active shutter glasses - but this would require you to buy a 3D Vision-capable monitor, as well as a new NVIDIA GPU.