What Phil said.....
I'll usually shoot night games in M. I'll position myself on a sideline, between the light poles. If you were to draw a line "vertically" through the center of the field- goal to goal for soccer- then the action on the closest half to you will be the best, and most consistently lit. Once play moves over that line, (away from your sideline) then the lights you are shooting under will start to quickly fade (inverse square law....). A similar thing will happen if you were to shoot from the endline. Once play approaches you and gets past the nearest light poles (usually about 25 yards from the goal) there is often no light on the player's faces. Look for action where the lights are best.
I have found the best way to control the exposure, as Phil noted, is to study the lights carefully.... To most players and fans- the whole field looks lit evenly. We have to know better. Once I am able to figure out the "sweet spots", I'll find an exposure manually that doesn't over expose the white team's jersey. It's usually a good bit under what the camera would meter. I suppose that could be done in one of the modes- AV, TV, whatever... but I've never had it give repeatable, consistent results that way.
White balance is a constant challenge. My experience is that the lights typically cycle through the color spectrum... so my 1/1000, or 1/500 of a second will have a mixture of dozens (guessing) of light bulbs, all at different points in the color cycle. Usually.... they average out nicely enough, but every so often, I'll get unlucky, I suppose, and get more of them on red or green at a given moment. I will usually shoot in raw, fix this later. No sense trying to set a custom white balance when it changes from shot to shot.
The good news is- you have captured good moments in your shots, and you have a nice enough combination of light and gear that you should be able to get the correct exposure. Fine tuning will make a great improvement in your results.