Air Options: You can only double jump, teleport etc. so many times before touching the ground again.

BURST: Fills over time and, as of 0.3.0, it also fills a little when you get hit. Used for Burst (100%) and for Whiff Cancel (50%).

Every hitbox color that isn't red is just there to signify when the hitbox isn't active.

Hitbox colors: 

• Yellow is the area vulnerable to damaging attacks
  
• Blue is what I assume to be the area vulnerable to grabs, if YH handles it like other fighting games do - the size difference between blue and yellow is so small that it's difficult to actually verify this in singleplayer.
• Red is the area where attacks deal damage

If the red collides with yellow (or blue, for grabs), then the attack lands.

and the red hp bar is the current damage delt in the "combo"

once you are able to successfully use moves again the red damage bar will be dropped, its just a visual to show the current damage delt to a player in quick succession
the black hp bar isnt black,  just transparent, black and red both are lost damage, while red is ^^^ black is just total damage (red goes over black damage until red is dropped, then the hp bar shrinks down showing more of the background)