I think it depends on the time zone set on your computer. I'm in Europe, time zone GMT+2, and the Duolingo day ends precisely at "my" midnight.
I am also in the USA on PST and my streak ends at midnight. -shrug- Did you start using Duolingo in a different time zone?
As far as I know, the cut off time is midnight of the time zone in which you registered your account (basically so you can't cheat by just changing the time on your computer).
No, the cut off adjusts if you travel to a different time zone.
For some reason I get a message about weekly leaderboard winner around 6pm on Sundays.