My MC kicks someone in the back of the head. Would the person be stunned, knocked out, or something else? Also, how long would it take to make someone pass out from blocking the flow of blood to their brain (via choke hold with elbow around the throat)?

Any kick to the head runs the risk of a concussion, knockout, or death. There’s always a chance, depending on the kick used, that the force of the blow will knock the skull off the spinal column (this is usually more of a risk with spin kicks like the wheel kick and jump kicks). How much damage your MC does to that person is going to depend on a few things:

1) How used to kicking they are, especially in the head?

There’s a difference in effectiveness between a character who practices three times a week and a character who almost never kicks and is doing it out of desperation. (The chances of them even being able to reach the head from a standing position if they don’t train their flexibility and muscle control is unlikely, but it can happen.) It’s worth remembering that most untrained individuals rarely think with their feet or legs in combat. If they practice a style that doesn’t have at least some focus on kicking, then it’s unlikely that they’ll think with their feet as an opening attack. A lot of whether it’s stun, knockout, even death will rely on how well the character does follow-through and (if they know what they’re doing) if they were holding back.

2) Are they (the attacker) standing or sitting when they perform the kick?

If they are sitting when the kick is performed, then it’s likely it’ll just stun as they generate about half the force. A character who is limber enough can kick fairly effectively off the ground and while they are seated in a chair (so long as they can rock the chair back onto it’s back two legs).

A kick to the back of the head (I’m assuming it’s a front kick as opposed to a sidekick) from a standing position will connect with the ball of the foot, a kick done from a sitting position could use the ball of the foot, the flat of the foot (the whole bottom portion), or the heel.

3) What kind of shoes are they wearing?

This is important, because for a head kick to work on the street, it requires more than just very good muscular control, balance, and flexibility. The clothing and shoes must also be amenable. A character in really tight clothes, especially pants will have a hard time kicking to the head because the clothing doesn’t allow for that level of flexibility. Really tight skinny jeans without any elasticity, for example, make high kicks tough.

Heavy shoes like combat boots or shoes that provide little to no support like flip flops and other kinds of sandals won’t be very effective. The power in the high kick or any kick that goes to the head comes almost entirely from speed. Now, there are certainly people out there who are very effective wearing any kind of shoe they like (forget about high heels), but it’s always worth considering all the factors including the ones that your MC will have no control over.

The choke you’re looking for is called (at least my school called it) The Triangle Choke. It has a few different variations on the holds (hands clasped versus hand behind head), but the basics of it is this: you’re not using the elbow, you’re using the bicep to cut off the blood flow from (I think) the carotid artery when you squeeze. And the answer is not long. If the choke is done correctly, only takes 15 seconds to kill. If the character is distracted, they really could kill someone without meaning to. When we practiced this hold, the minute we felt it working was cause for an immediate tap out.

Things to remember about this choke:

The character who is performing the choke must be higher up than their victim, so it’s a good idea to knock them to their knees or make them stumble first. This can be done easily by simply stepping on the back of the calf to drive the other person to the ground. A taller character has to worry about this less, but it’s going to be a concern for a shorter character and something that they’ll have to work around. The choke itself is fairly difficult to execute if the character has never practiced with it (it has something to do with the alignment of the elbow and the victim’s jaw), they’ll need at least a few sessions of practice in a controlled environment before they get comfortable with it.

Anyway, I hope that helps.