There's another strategy for the first skip that is about equally difficult. You can bounce at a weird angle off the bottom right corner of the horizontal platform to the left of the teleport (you can use the cannon's light as a guide) and into the switch on the right.

Whether a given level is unlocked is determined solely by the number of crystals you have. Diamonds and rubies don't count toward that, unfortunately.

At least, i assume it's new since i didn't see it in the few submitted runs that i've looked at.

Specifically 0:08 - 0:12. You can use one of the soul-activated platforms to the left to launch yourself over a gap.