Combined cycle turbines do have a steam component (that's where the word "combined" comes from). The waste heat from the combustion turbine front end is used to make steam in the back end.
Combined cycle turbines are not primarily powered by steam. It is a secondary consequence of their operation. This contrasts with nuclear and coal plants where steam is the prime mover.
The steam part of CC systems shows hours and hours aren't inherently needed to get a steam power plant in operation. For that matter, warships with steam propulsion show the same thing, I believe.
In some cases yes. Modern combined cycle plants can take as little as 30 minutes to ramp to full output. Older designs can take upward of 4-6 hours.
If you have steam as an indirection, that's when things take a really long time. Natural gas turbines are a more direct cycle.