You only check the power of the other creature when it enters the battlefield. --If it's 2 or less, the ability will trigger. Once the ability triggers, raising that creature's power above 2 won't affect that ability. --Similarly, reducing the creature's power to 2 or less after it enters the battlefield won't cause the ability to trigger.

Apply power bonuses from counters the creature enters the battlefield with and continuous effects like Mayor of Avabruck's when checking to see if Mentor of the Meek's ability will trigger.

You choose whether or not to pay when the triggered ability resolves.