How is the heel kick executed? Is it similar to motion of the straight leg outside crescent kick?
In answer to your last question, the heel kick motion is similar to the motion of the straight leg outside crescent kick.
For a lead (front) leg heel kick, lift the knee upward (at least hip high) and backward toward the opposite side as far back as it will go comfortably. As the knee lifts, the shin lifts with it and ends up parallel to the floor with the foot pointed toward the target and also parallel to the floor. This completes the chamber.
The kick then fires to a point about 12 inches to the outside of the same side of the target. To fire, the body, hip, and leg muscles push the knee (do not think about the foot or leg, think about pushing the knee toward the target) forward in a straight line (think of the leg as piston on its power stroke) and, as the foot approaches the point to the side of the target, the knee straightens and stays straight (but not locked) as the body, hip, and leg muscles and twisting of the body push/pull the leg sideways into the target with the back of the heel making contact. The foot, hip, and body remain in a straight line and move as a unit as the foot moves into and through the target. The knee stays straight until the knee is pulled back into the original chamber position. From the chamber position, the foot may be returned to the floor, or another heel kick or a different kick may be fired.
The heel kick is executed in the same manner as the hook kick, except for the motion of the straightening of the knee and the alignment of the foot, knee, and body as the foot moves into the target. In the hook kick, instead of the knee staying straight, the heel is pulled backward toward the butt while the upper leg, hip, and body keep pushing and pulling the heel into and through the target. In the heel kick, the knee stays straight; in the hook kick, the heel snaps backward as the knee whips it into the target.