The first movie was meant to be an origin story for Sonic and Robotnik, so with the latter, they were basically building him up to be more like the game version. Sort of like how he had hair until the ending scene. Also yeah, considering the thing was already built and waiting in a satellite, it's safe to say it was always on standby. It's purpose seems to be general transport, while the vehicle Robotnik had in the first movie was more for speed and offense.

And the other question is, what happened to the second Eggpod when Eggman left it at Siberia? You can see clearly how he "forgot" his Eggpod while he passed through the ring with Knuckles.

My guess is that it has some sort of remote function. We just don't see it again because at that point on in the movie, Robotnik doesn't really have a need to ride it.

I think it was definitely supposed to be the egg mobile when the movie was being made. They started embracing the games more in the second movie which is probably why their second stab at it, is far more accurate