The commercial states that this ship is one of the fastest and most agile in its class. However, once you try it in game, it handles like a turtle. Is this a bug?

It is intended to have agile handling as described. The current handling is a result of a bug in the current IFCS system that affects all ships randomly. The Arrow seems particularly prone to this bug, but cycling the landing gear often fixes it. We're working towards making the Arrow true to its intent.