The credits aren't "dropped" by certain enemies; rather, all the participants in the battle are evaluated, a 'top' and a 'runner-up' (literally a 'valedictorian' and a 'salutatorian') are selected. The valedictorian might have a 70% chance of getting Support X, 30% of getting Support; the salutatorian might have 50% and 50% for those, respectively, and then the rest of the honorees have smaller percentages. The top two honorees' chances always sum to 100, implying that they get one or the other, but the other honorees' percentages sum to over 100, so it might be that the top two are guaranteed one of the special credits and then everybody gets the other credits with certain probabilities. I'm still trying to understand it myself.
I'm also still trying to figure out how the soldiers are evaluated (i. e., what earns them points -- it feels like there are a lot of positive things you can do that might not, as baseball fans like to say, show up in the scorebook. A Scout who runs out into the field and reveals the presence of a tank in the distance before returning to behind the sandbags while a Lancer takes two CP to get behind that tank and shoot its radiator clearly deserves the 'assist' on that kill even if he hasn't accomplished anything that will earn him points.
Rescuing fallen allies seems to earn you a lot of points, as I once had a valedictorian who never fired a shot -- he did, however, run through covering fire to touch two downed allies.
I've been trying to give "playing time" to as many soldiers as I can in each battle so that many people will pick up credits. Typically I'll have 11 or 12 people obtaining at least something when the battle is over.
(Credit names, incidentally, are a little more informative in the Japanese version, where they do a better job of sounding like something off a college transcript. The "X" credits are in fact 優 (yū), which corresponds to an A in the Japanese grading system.)
As for how material drops work, let me spend some more time with the book and see if I can find anything. Having basically done all the missions in the order they appear, I've been acquiring material steadily and have usually had the right ones in hand when items requiring them become available.