Behavior beyond the critical pressure I have seen some phase diagrams that look like this:
https://www.learner.org/courses/chemistry/images/text_img/phase_diagram_water.jpg

And also some like this:
https://en.wikipedia.org/wiki/Phase_diagram#/media/File:Phase-diag2.svg

My confusion is related to the Critical Point. The first picture doesn't really explain where the gas/supercritical fluid boundary is, and the right angle indicating the supercritical fluid boundary at the critical point seems unusual to me. I have some general questions about behavior beyond the critical temperatures and pressures.

I think my specific question is best summarized by this picture.


More specifically, suppose you have an arbitrary compound X with a Liquid/Gas critical temperature of 320 K and critical pressure of 40 Bar which follows the general shape of the above phase diagrams. I have the following questions

1) At 330 K  and 10 bar (basically beyond the critical temperature but below the critical pressure) would X be a gas? or would it be a supercritical fluid? Would we need more information to be able to decide? 

2) As a more general part of 1), is it possible that a gas exists beyond its critical temperature?

3) At pressures above its critical pressure, a liquid can still exist so long as it's temperature is lower than the critical temperature correct?
In order to be in the "critical state", both temperature (x-axis) and pressure (y-axis) must be above the critical point. So answers to your questions become quite obvious:


Very hot but below the critical pressure, it is a gas. You don't need any more information than the temperature and the pressure.
Yes if its pressure is less than its critical pressure
Correct.