Birthday Triangles

It's my birthday, and I tried to find a puzzle related to it. I was hoping to find that my birth year and the current year (1998) could both be used as two sides of a Pythagorean Triangle (a right triangle with integral sides), but that was not to be. But luckily, I was able to determine that there will come one (and only one) year when my birth year and the current year are two of the sides of such a triangle (I'll be an even age, as I am now, but I'll not yet be 100 years old.)
  1. How old am I today? (I'm not 22.)
  2. What birth year this century can be used in the greatest number of such birthday triangles? (Where the birth year and a greater year within 100 years are both sides of a Pythagorean Triangle.)
  3. What birth year next century?

Source: Original.

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