1. No. But it helps. I am horrible at math, i just don't have the patience to work things out like that on a piece of paper that gives no feedback (like a compiler does). Most CompSci heads are actually good at math, but most Math heads are not good at programming (something about i = i + 1 ;)). When i was a CompSci undergrad, i was told that i was "the exception to the rule", because i was one of the top students who couldn't get more than a 'D' in Calculus 2.
2. I think so. But know that you said 'Computer Science', not programming or software design. CompSci can both improve and hinder your programming and design skills. It's the fundamental difference between Academia and The Real World. For example, you get your Bachelors ... you get a real world job. You get your Masters ... you get a higher paying real world job. You get your Doctorate ... and you get kicked out of the Real World.
3. Yes, but i don't think it's as "black and white" as you might think. FORTRAN obviously requires some knowledge of mathematical formulas, and BASIC requires little math at all - until the problem involves math. The better question to ask, IMHO, is "Will those with a good mathematical background go farther in programming than those that don't?" And that too depends upon what kind of programming you are talking about. If all you do is fetch database query results and slam them through the HTTP protocol, then no ... you don't really need a strong math background. But, if you want to get into functional programming, then a good knowledge of lambda calculus will surely help. At some point, you are going to have to be pretty decent with Math to move to the "next level". This is why i occasionally brush up on my Algebra, Trig, and Calc skills. While it hurts my brain sometimes, it surely doesn't hurt my programming skills. ;)

jeffa

L-LL-L--L-LL-L--L-LL-L--
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B--B--B--B--B--B--B--B--
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(the triplet paradiddle with high-hat)