The corner jumps aren't hard, you just need to cut down on your angles when you jump. Making a 90 degree turn in the air is much harder than making a 110 degree turn in the air...so just watch your angles.
It's best not to try sprint jumping or jumping from a standing position with the 2 drop downs. If you walk & jump from the very edge of the platform it puts you really close to the doorway. You can also jump into the fire, then drop down into the doorway...but it's slower...and probably harder than mastering the jump directly into the doorway.
If you do parkour...you should already be good at wall jumps. Again...you just cut down on the angle as much as possible, and make sure you're sprint jumping as far out as you can.