Why have we not found anything remotely similar from that time?

Most artefacts don't hang around for more than a handful of decades; when you get to twenty-one centuries, you're lucky if anything survives. This is especially so with something made of an infinitely recyclable material like metal. The only reason this one was found is because it was in a shipwreck.

Who do you think made/used it?

It's marked with the Egyptian calendar, so it would have been made for an Alexandrian astronomer, or possibly exported by an astronomer who lived somewhere else. Alexandria was an important centre for that discipline. Its most famous luminary is Claudius Ptolemy, who lived a couple of centuries after the Antikythera device was made; another is Sosigenes, who would have been roughly contemporary with the Antikythera device and was responsible for the design of the Julian calendar.

Could there have been lots of them used at that time and if so, what does that say about the era's technological state?

It depends what you mean by "lots". If you're asking whether it was a standard piece of household equipment, then no. But there were a fair number of people studying astronomy who would have a use for it. I don't find it too hard to imagine that something like it would have been a regular sight among the equipment of researchers; but its complexity, and the consequent expense of manufacture and calibration, strongly suggests that it wasn't as common as, say, the mediaeval astrolabe.

Why was there a gap of centuries until something as intricate was invented?

There's no very good reason to suppose there was a gap of centuries; as I mentioned in answer to your first question, artefacts tend not to survive very long. Absence of evidence is not evidence of absence. Astronomy as a field continued to be well-studied for centuries after the Antikythera device was made, and there can be no doubt that someone like Ptolemy had access to equipment that was at least as sophisticated. Alexandria itself faded as an intellectual centre from the third century onwards; and the eastern Roman Empire diminished and had a deep economic and intellectual downturn in the 5th to 8th centuries. From about the fifth century onwards, then, new research into astronomy basically disappears from the Greek world, and that would mean no more market for equipment of this kind.

This documentary: http://www.youtube.com/watch?v=yciB8gS9aYU indicates that inscriptions on the mecanism had been read and it use the corinthian calendar, so it would probably come from a city using this system. Syracusa used this calendar so it is a clue to link the mechanism to Archimedes. And Alexandria used the macedonian calendar, where the names of (at least some) months (greek calendars are a freaking mess), are different, but who knows it was maybe a copy of an original using the corinthian calendar. The place of the shipwreck is on the road between italy and eastern greece or Asia minor-Syria, a ship who would go to or from alexandria would probably take a more direct way.