That's correct about the pullups as far as I know (pull-up is palms facing away, chin-up is the opposite), but my OSO told me you can do it either way for the PFT. On the other hand, almost everything you'll encounter at PLC/OCS will be using overhand grip, so it's good to train that way.
Here is the ab routine. It's ten exercises, and you should start doing 10 reps each. The routine takes about five minutes, but is very effective. Increase the number of reps when it gets easy.
1. Regular crunch. Cross fingers behind head, you should not be able to see your elbows out of the corner of your eye.
2. Lat crunch (right). Same as a normal crunch, but lay your legs over to the right side to work your lats.
3. Lat crunch (left). Same as #2, but legs to the left.
4. Legs up crunch. Raise your knees so your lower legs are parallel to the floor, and cross your legs at the ankle. Place your palms on the top of your head, elbows together in front of your face. Now touch your thighs with your elbows.
5. Superman crunch. Lift your legs up perpendicular to the floor and keep them there for all ten reps. Now touch your toes.
6. Straight leg lift. Lift your legs perpendicular to the floor, then low them. Your hands should be on the floor at your sides, and your feet should not touch the floor on the way down, just hover slightly above the floor.
7. Leg crunch. Put your legs out straight, then bring them in to your body, like the position for #4 (only not crossed).
8. Butterfly crunch. Put your legs on the floor with the bottoms of your feet touching. Now lift your feet in toward your chest, then lower. Try to get your butt off the floor, too.
9. Bicycles. Pretty self-explanatory. Like #4, only you're touching opposite elbows to opposite knees. Each elbow to the opposite knee once is a rep (so left, right, left, right, etc. for ten times each side).
10. Full body crunch. Basically combine #1 and #7. Bring knees in and upper body up.
Remember that your abs are like any other muscle. Make sure to rest sufficiently between workouts, remember to stretch, etc. A good stretch for the abs is to lay down on your stomach, then raise up on your arms while arching the back. You should feel a nice stretch.