Roger that on the crazy pull up counting. On my inventory at Seniors I did eight, then went up for the next one and the instructor counted "one". General rule, if you don't hear them count it out loud, it doesn't count. Get used to doing them so that your chin cleans the bar by at least an inch or so.
Also, a really good drill is to do a wide grip dead hang at the end of your pull up sets. Basically get your hands in a wide grip, pull up, and hold yourself there as long as you can without using your chin. Fight it the whole way down, even if there's only a tiny bit of flex left in your arms. Once you hit the bottom try to bang out as many pullups as you can. It will probably be 3 at most. This drill helped me increase my pullups considerably.
Also, bear in mind that if you haven't been doing pullups, no matter your body type, you will probably be able to do more reps at first with your palms facing towards you and your hands together. However, as you progress, you will probably find that you can do a lot more using a wide grip with your palms facing away from you, if you train properly. I'm too lazy to try to explain the physiology of this but anecdotal evidence suggests this is true for about 95% of the Marines I know.