Couple of comments.....ignore if you like.
First, Dont fire with a YAK outside of 400, even 400 is pushing it. Those 600 and 800 shots are just wasting what little ammo you have.
Second, you have got to look around more. That Yak was after you once you turned off him but you didnt look back until rounds were bouncing off your plane! In a furball like that one you should be spending more time looking out other views than you do looking forward. Are you using the keyboard to look around or a hat switch?
Third, in a furball like that one you dont want to spend more than a second or two on any one target. The longer you do the better the chance that someone is setting up a run at YOU. Dive in, pull for your lead, shoot a burst, and break off the target. Repeat as long as you have ammo and E.
Forth, the Yak at the end of the fight, you either have to choose to fight him, or choose to run. You seemed to be in the middle. You were maneuvering too much to run, and not aggressive enough to fight. Yes you got a couple overshoots but that is because the yak was aware there were other enemy and so he was trying to hold his E as much as possible to escape any attackers (which he did a minute or so after he left you to land 3 kills). If your running, point your nose away from the furbal, and fly looking out the back. When you see tracers roll left and right a bit to help him miss, but dont go up+down, or touch the rudders. Keep the plane as clean and smooth as possible to out pace the enemy until he get bored or help comes to save you.
To fight, get aggressiv, break in one direction and chop your throttle as he closes hammer the throttle and roll back into him. Most guys keep their throttle full, by chopping your throttle you can get an advantage in turn rate with a slower speed. He's going to be burning E trying to keep ahead of you, so chopping your throttle wont hurt that much. During that whole instances of the fight you should have used your views to keep him in site at all times. This way when you did get an overshoot you could kick a rudder to get a close up shot as you pass. In most cases, "lose site, lose fight!" You cant shoot him if you dont know when hes going to pass in front of your play.