A:AnswerNo, for 2 reasons.
1. PS4 runs at a 60hz refresh rate.
2. A Display Port is needed to achieve 144hz if you were to use it as a PC monitor.
Still a viable option for a PS4 monitor though! Although you're paying for more than you will be able to use if you're only using it for the PS4.
A:AnswerNo, and you won’t be able to play 1080p 120hz either because this monitor only supports 144hz through DisplayPort or DVI port. Do not buy it for next gen consoles because consoles use the HDMI port.
A:AnswerThat all depends on your graphics capabilities. The refresh rate on your computer correlates with your frames per second. Let's say you get 80fps on a game, the only way you can actually see all of those frames is by having a 75hz, or better, monitor. I would fully recommend the Asus VG248QE sold by Best Buy, it's even on sale. It offers a jaw dropping 1ms response time, 144hz and an unbelievable 80,000,000:1 contrast ratio. Honestly the visuals are the best I've seen on a monitor from its class. You simply will not be disappointed.