In Carcassonne, how does the Bazaar play and count in different situations?
Yes,

Per the Carcassonne Annotated Rules, the Bazaar ends a road, although it is not directly stated.


  It seems clear that a bazaar ends a road in the same way as a crossing or bushes


The Bazaar itself is not a feature that a meeple can be put on.  It does not count as a cloister.  It doesn't change farm or city scoring.