1. Just to make sure you're doing right, you have to tilt the Left Stick towards the direction your attack is coming from and not press it. I find the timing is close to Witch Time so you might want to time attacks based on that. Another thing you can do is flicking the stick towards the direction several times, quickly, if you haven't nailed the timing yet. Works sometimes, but not always.
2. Perfect parry is pretty much identical to Bat Within, i.e. you press in the direction the very instant you are going to get hit. The standard parry has a very wide window to get it, you can just tap towards the enemy and you're near guaranteed a parry. When I wanted a feel for it, I loaded the game on Very Easy Chapter 1 and took the automatic accessory off. Fight until you face the Beloved in the Courtyard and try and perfect parry all of his attacks. If he hits you, it's no biggie as your health regenerates and you take little damage. Then take it from there, trying it on enemies on Very Easy. It's the perfect mode to get used to it.