Best thing to do to improve your mile time is to run very hard days with recovery days in between.  Try doing speed ladders.  Speed ladders are where you start off at a smaller distance (100-200 m) and then work up the ladder (increasing distance 800 m) and then back down.  An example would be (in meters) 200-400-600-800-600-400-200.  Set small (1-1.5 min) recovery times in between runs but increase them as the distance increases.  Or you can do intervals such as 8x400m or 4x800.  Best thing to do though is to switch it up on hard days and to try not to do the same workout on hard days every week.  On your recovery days try running for at least 40-45 min or so at a conversational pace.  This was my schedule during track this winter.

Mon-hard, Tue-recovery, Wed-hard, Thur.-recovery, Fri- Meet (test yourself on your improvement). Also try to run on at least one day of the weekend.

Through these workouts I dropped my mile time from about a 6 min mile to a 5:37 mile in about two months and I'm looking forward to more improvement.  Running is one of the most time consuming things to improve but if you keep with it and push yourself to the limit, you will only see improvement.

You're on the right track!  The Academy sites mention somewhere that a good foundation in Algebra is better than exposure to Calculus.  However, you answered your own question--take the summer class too.  In fact they like it if you take a computer science or prog. class as well.

Lots of H.S. activities, volunteerism, and leadership roles.  Push yourself to extend your leadership capabilities.  Stay focused.  Prepare for your interviews with the Liason Officers and the Nomination committe by thinking of dozens of questions they might ask you and practice answering them.  Have a smart friend listen and critique.  Tape yourself.

Most importantly be yourself and let your answers reflect how you really feel, not how someone thinks you should feel or answer.  Be passionate and clear.

Character matters--make sure yours is squeaky clean and that you are an honorable person--read and memorize the Air Force Code of Honor.

Good luck!