1) This isn't surprising - it's just the baby boom generation.
Oddly, no. If WikiPedia is right, the peak birth rate for the post-second world war Baby Boom is well after 1951, among a cohort who have won fewer, rather than more, Hugos and Nebulas.
2) What happens when you shift your dates to 43-52 or 41-50 or 39-48 or whatever? Because this all seems very contrived and somewhat meaningless to me.
Since you asked, these are the figures of Hugo and Nebula awards won by year of birth from 1937 to 1956:
3) Could this anomaly be explained by having one or more outliers in this age group skewing their combined ratio enough to stand out? I'm thinking here of Connie Willis, who has won rather more awards than your average Hugo or Nebula award winner.
Makes less difference than you might have thought. Connie Willis, with her 15 awards, was born in 1945; so, however, were 8 other award-winning authors, none of whom has won more than two (Michael Bishop, Edward Bryant, Jack Dann, Gordon Eklund, Eileen Gunn, Elizabeth Moon and Janet Kagan) and I reckon that flattens the curve. Only one of the other four authors with ten or more awards was born in my 1942-51 range (Joe Haldeman); the others were all born earlier (Poul Anderson, Ursula Le Guin, Harlan Ellison).
If any cohort's statistics are inflated by a couple of outliers, it is in fact that of twenty years later: four authors born in the 1962-71 range have won ten Hugos and Nebulas, and two of those four (Kelly Link and Ted Chiang) have won four each. (By contrast, twenty years ago, the 1942-51 cohort had already won 62 Hugos and Nebulas between them!)