1.A) Approximately. (Originally this was yes, until you stated that there were at least 700 million people on the planet. After that information, I updated this answer, because I realized that the problem had an additional assumption of a finite number of people, thus encountering any one left-handed person reduces the odds, very very marginally, of any different future person I encounter being left-handed, because the pool of people I'm drawing from now has slightly different odds.)

1.B) No. (Still.)

1.C) Approximately. Why the answer is different without resorting to math: In 1.B, we nonrandomly pull 10 right-handed students out of the group. In a pool of 24 10-sided die we've already rolled, we've pulled out 10 of them which did not roll 1; this does not alter the number which did roll 1, increasing their relative proportion. In this case, we've rolled the dice 10 times, and they never came up 1; the remaining 14 times remain fair dice rolls.

1.D) (Modified) Approximately.

1.E) Very very slightly.

2.) [Edited; apparently I screwed up when I added the possibility of an exact match] .41%, still assuming we're not considering the proximity of 0 to 3, and including closer matches. (That is, only considering identical digit matches.)

3.ab) Supposing it's more likely that a higher quality student is A than !A; it's possible that it's extremely unlikely for a person who isn't high A to have high grades while still having more high grade students who aren't A than are A, if the odds of A are substantially lower than the odds of being neither A nor B but still having high grades. So there's not enough information.

Assuming it's more likely you're A and have high grades than ~A and have high grades, however, and assuming that this distribution holds for the grade average for each college (p(A|G) > .5 for all three G), you should in all cases favor low-B students, because the remaining pool of accepted students is more likely to be A than !A, because !B limits you to the pool of students who are either A or !A with high (enough) grades, and A was already assumed to be more likely.

But we don't really know p(A|G), either for low, average, or high grade levels from the problem description, so I couldn't actually say.

ETA: That should really be p(A|G!B), because, while A and B are independent variables, G is correlated with both. But I think everything still holds anyways.

4.) 35%; expected utility is p(A) times A, which leaves us with 1*10 and .35 times 35, or 10 and 12.somethingorother. We have expected returns of $12 for the 35% case, which is higher than the $10 case.