The odds depend upon comparable houses or condos being sold at prices that are lower than your property assessment. When you appeal it you attach evidence of comparable being sold at lower prices than the assessment could change.

Not sure of NYC but I would contact brokers there to find out

It goes up but not annually or obviously stays the same. The only way it could go down is during a property tax assessment. Property assessments correlates wih property taxes. Housing prices assessed last year or two were super high but they are now coming down so I plan on asking for a reassessment in the next year or two to get a lower assessment but it could not work out too. Hope that helps