I don't have any specific knowledge of the process but here are some answers as I see it....
As a non american, can someone explain what these hearings are for
The hearings are for the New York state government's regulating body to learn more about (virtual) crypto-currency so they may understand it better as a whole before deciding whether it specifically needs more law/regulations concerning it. This government body asked "representatives" from law enforcement, commerce, and academia to publically testify and answer questions to this end.
how they play in to the US legislative system?
New York state is an important financial center for the Unites States and arguably the world.
Who is the intended audience (other than curious bitcoin holders) of these hearings?
Well, theoretically it's for New York residents, however because NY is so important understandably the world may be curious. How New York decides financial regulations is understood to possibly affect how other states may act, and even possibly federal actions.
Why are they being held in New York, not Washington, and what's the relevance of that?
Washington DC is important federally (for the country); New York is important regionally (state). However since this is financial regulation within New York state it could be construed as important not only federally but globally since arguably some other countries may look to the U.S. regarding financial regulation.
Also, what's the output from these hearings?
The output is uncertain. It could lead to new law, amended law, or nothing. If nothing else it certainly is serving to help government better understand how important Bitcoin is.
Will the chair/judge(?) produce some kind of report with conclusions?
I would assume there is a 100% likelihood some document would result from this hearing however conclusions may come as proposed laws/amendments. I would guess it's possible if they decide not to act at all they may issue a statement to that effect.