Question about ASUS Mx34vq

It seems that someone has not been properly informed, because the monitor has 100hz and AmdFreeSync in the range of 48 to 100hz, so you can also use it very well for gaming.

If I get a Gsync display for my PC, can I also play with the PS4?

No. It has neither G-Sync nor 100hz like e.g. Acer Predator X34 or Asus PG348Q. This monitor is only suitable for editing or for media people.