The center is the smart area to cover in doubles as it is the higher percentage play for your opponents to hit to. If they are going to burn you make them hit the harder shots. Plus if you are the one controlling the center it probably means you are the one doing the poaching and putting pressure on your opponents to do harder things.
Play the ball, well, not 100% sure. I know if you let a ball play you it typically means you let the ball get too far out of your sweet spot and you are jammed or stretched trying to hit the ball. A good example is when someone hits a kick serve. Move to it early to cut down the amount of sideways movement the ball will do the longer it is in the air. If you wait for the ball to come back to you it will keep moving more and more sideways and it seems as if the ball is playing you and you are not playing the ball.