Interesting question. Zeus was the son of Chronos (king of the Titans) so technically he would be a Titan, but I do not recall him ever being referred to as one.
As far as immortal, yes, Zeus was immortal as the other gods. He was not omnipotent (an important note) and there is the implication that he could be killed (by his fellow gods if nothing else).
By what standard was he immortal? He seemed to have stopped aging, but his powers again were limited (mostly to the sky. Which meant he was still pretty darn powerful).
Zeus was a god. The Titans were immortal too, though. The big difference is that Kronos, Zeus's father was a Titan