The heart rate being a telling sign of the sex is an old wive's tale. At my 12 week doppler, the HR was 169. Since then, the HR has never been below 140 (which according to this theory, would indicate a girl). Well, we've got a boy & so does a friend of mine whose 12 week HR was 164.
As far as 2nd tri, I've heard 14 weeks. (That's assuming one's follicular phase was 2 weeks, making the gestational age of the baby being 12).