Here are my thoughts. They're not problems, just things I noted.
One thing about initiative and awareness check. Don't fail it. The combat could have been over before Subotai or Dubai reacted. It's even more important than in other systems, because of those counter attacks.
For example, in a 2 vs 2 combat, a player could do 6 attacks before the second one plays.
Turn1
2 enemies attack player 1: 2 reactions for player 1
Player 1 turn: 1 action
Turn 2
2 enemies attack player 1: 2 reactions for player 1
Player 1 turn: 1 action
Player 2 turn: 1 action
On another hand, combats are very fast because of this. So don't fail awareness checks
Another thing about awareness. You ask us to throw it in advance which is a good thing, but I have a question.
lets assume the DM ask for a check. Players should throw 2D6
under skill+adv skill. To avoid an incoming trap for example. Mainly against environmental hazards I suppose.
But, if it was to spot a sneaking enemy, players should have to throw 2D6+skill+adv skill
versus enemy sneak.
It is two different throws to do in Coyote Code. And the players don't know which one to do (and shouldn't know, obviously).
So, perhaps the players always throw 2D6+skill+adv skill and the DM sort it out.
About the reaction system (when you have to counter attack), it is great. It gives a nice feeling of exchange and uncertainty. But if I understand well, number is not an advantage here. In a 6 vs 1 combat, it could end in 1 round with the 6 men dead. It reminds me samurais movies, when you don't even understand how he managed to kill everyone around him in the blink of an eye. Let see how it runs.
And finally, it's a good thing we are all very present (partly because it's a new game) because the DM has to wait for the player's counter attack to solve every attack he makes. If it becomes a problem, perhaps you should throw those one your self?
Anyway, I like it so far.