1. You can use both, AV or Manual. For AV (Aperture Priority), your Shutter speed may vary (usually not by much), depending on the Camera's Metering reading and ISO setting. For Manual, you can set-up both the Aperture setting as well as the Shutter setting prior to you taking the pics..
2. Yes, f2.8 should be fine. And yes, use AI Servo Mode as you will be tracking and following moving objects/players.