Hey!
I'm really sorry you struggled with the game. Hopefully I can explain the mechanic and make it a bit clearer.
For the wall run: It's definitely possible, make sure you are hitting the wall just before the peak of your jump, and hold into the wall. You will know you are actually wall running if your camera tilts.
Also, if you are finding yourself always falling off, you can hold space after your jump to launch yourself up the wall.
I have a video of me speedrunning the game here, check it out for any section you are stuck on.
Thanks :D