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The current fixed calendar is arranged (by adding or taking out an extra day in Marcheshvan or Kislev) such that Yom Kippur can't fall on Friday or Sunday (so there won't be two days in a row where no work at all can be done) and such that Hoshana Rabba can't fall on Shabbat. Most months are of fixed length, so this effectively limits all holidays in some ...
Check out hebcal.com -- it has exactly what you need for the second option. There's also code you can use to script something that will tell you whenever Pesach lands before the Equinox. I'm personally partial to hebcal-js, having written it myself. ;)
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