It is also a feeder court for the State's Supreme Court--which, despite the name, is the trial level court of NY (think of "supreme" as meaning "superior"). If you serve well on Civil, you frequently move up to Supreme.
Just an FYI. This is a real court, a real judgeship.
Yes it is. But it isn't a criminal court. It doesn't handle constitutional issues. It handles small civil cases. I don't see where fear of Sharia enters into it, but as you pointed out their cases can be reviewed by the state Supreme Court so if this judge does inject Sharia law into her decisions they will be struck down on appeal.