So, I made the movement for the opengl compliant backend render engine, so if it's slippery, I can bump down the inertia and base speed pretty easily. Obviously there's no tutorial (yet), but you have a couple of options to get back up:
1: Put yourself between two buildings or a corner and use the wall jump mechanic by running into the wall in the air and pressing spacebar
2: The rocket launcher can be used to rocket jump with varying degrees of health loss
3: The leech shotgun has a backblast for clearing large jumps, you can just point down and short cycle the animation by rapidly clicking to fly, but it takes away your health.
4: The teleporter sends out a little disk by clicking leftmouse, and you can teleport to it using right mouse. If you can alternate between time two, it lets you move pretty much anywhere in the map, but it breaks your in air combo meter (which doesn't yet have a visual representation so don't worry about it lol)
also you can crouch with shift and jump out of a crouch for extra height. Crouching midair will make you fall faster. You can navigate some pretty large gaps by using crouch jump and the double jump, then running against a wall.