How fast does a person grow old, in in-game time?

I noticed that after a certain size, around 30k population, my city's population growth rate declines a little without expanding residential zones. I then briefly looked around the houses in my residential districts and saw that a good number of homes had seniors as residents. This was around 20 years into the game from the start.

How long does it take for a person to grow up?

It takes about 2 years of game time for your first senior to appear in game. My first senior appeared after about 2 years of the first citizen moving in. I do not know if its is a variable amount but that's what I experienced while testing.

From Wiki

Citizens age very quickly in Cities: Skylines, with a typical lifespan of 6 in-game years.

http://www.skylineswiki.com/Citizens#Age