You want to change your focus to AF-C , page 54 of your manual tells you how. You can also switch to the Sports mode. Shutter priority in action shots is better than Aperture priority. You may get less DOF, but you will get nice action shots.

#2 looks like it was shot before the focus locked on.
#3, was it really dark enough for ISO 1600?

Good luck!

Pj