Sprint Jump: Running and jumping repeatedly while releasing sprint mid jump and reengaging it upon landing. Essentially doubles your movement speed and mitigates stamina loss. You can move the mouse to somewhat control where you're going in midair

Pause Falling: Pause the game at any point when near the ground after falling from a great height to prevent getting any sort of fall damage.

Any advice if I'm struggling with the barrel jump to skip the key?

You need to land on one of the barrels so you don't get stuck, then try to get as much forward momentum as you can by sprinting slightly and jumping over the gate. As long as you target the gate, you'll be fine, but try not to hit the fence while doing it. It took a lot of practice for me to get consistent at doing it.