I have purchased a Hampton Bay Huntington III 52in Ceiling Fan
In addition I purchased a speed fan control to use with this Ceiling Fan.
The Fan control is for 1.5 amp ceiling fans.
Does the Hampton Bay Huntington III
52in Ceiling fan meet this 1.5A requirement?
:)

The 1.5 is NOT a "requirement". It is a limit of how much the wall control can... control.
The wattage or amperage will be on the label on the top of the fan motor.

I guarantee you are fine. A fan motor over 1.5A is vary rare.

Does the fan have lights, and are they on a separate switch?

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More