How long do leagues last? No demotions and no resets will just break the system

Yeah

https://www.chess.com/announcements/view/how-do-you-feel-about-players-league

https://www.chess.com/survey/how-do-you-feel-about-chess-com-players-league-earn-trophies-to-go-from-wood-to-legendary

But there are new players joining the site every day, so there will always be accounts in the lower levels and multiple divisions.

There are the following

• Wood : 271,855 
• Stone: 234,350 
• Bronze: 400,463 
• Silver:  1,030,126 
• Crystal: 923,759 
• Elite: 270,067 
• Champion: 57,104
• Legend: 2,692 

Looks like a pretty decent distribution, centered around the middle Leagues, which seems like it should be expected, and since the feature has been live for 4 full months, I don't think there is a very high likelihood of things getting top-heavy. I could be wrong though.

Well compared to the original competition it's much, much, much easier to pass 

do leagues reset at the end of the year and we all return to wood or we stay at the same league?

There's currently no resets or demotions. Though it's always possible that will change.