How does parrying work?
From my experience, you will be unable to parry (despite the prompt making you think that you can) if you are still carrying out an attack. This has been the most common reason I've failed parries.
I can confirm that what direction you are facing will not prevent you from being able to parry an attack, as I've parried attacks that were coming from behind, simply by holding the Square button. As long as you have the Square button pressed when the attack hits you, you should parry successfully.
The time window varies with enemies, as they attack at different speeds. For instance, I've parried the Slime-type enemies (Flan, etc) by holding down the Square button as they approached and it's taken up to 10 full seconds before I actually parried (if not more) as they approach very slowly. For faster enemies like a Coeurl, you will have less than a second to react, and, from experience, if you're mid-attack at all, you won't make it. Using quick weapons like the shortswords will give you a better chance to successfully pull off a parry. Using a greatsword, on the other hand, results in very few successful parries.
As to whether or not parrying is worth it, definitely. I have survived many fights that my party members have all died during simply because I stopped attacking and just parried everything I could.
From my experience attacks that can be parried have to be targeted at Noctus only. I have not personally seen any sort of swipe or AOE attack able to be parried. When you see the parry button on your screen you can hold down the button any time during that button to parry the attack, you might be having problems with other enemies attacking you while you are holding the button causing you to stagger and not able to parry. And to answer your last question parrying is extremely valuable to combat, when you parry you may be able to perform a link attack with another party member. Another bonus is that breaking appendages and making enemies vulnerable seems to more common when you do perform parries on enemies.
Hope this helps.