I was wondering if it's possible to change the start date in Gal Civ 2 TA games?
No, that is hardcoded.
And have specific planets colonized already before game starts. For example, humans colonize Mars in like 2100, then Venus in 2150. Then have these colonies ready and running by the first turn of the game?
The only way to do this, that I can think of, is a custom map. However, that is probably too much work, because you would need to predefine all races on the map, and recreate their home-systems. Not to mention the map itself, with all the stars, planets, galactic resources, and asteroids.
One thing I don't get is why GalCiv never gives Jupiter or Saturn habitality.
You can only colonise planets in GalCiv, not moons. It is possible that either Jupiter or Saturn, or both, may turn habitable due to a random event or a UP proposal, but that isn't guaranteed.