Questions about: power

Have you read the manufacturer's documentation? The switches in the remote likely are for setting the transmitters frequency, and have nothing to do with fan speed. Usually fans have a speed selector switch (pull chain) that allows you to select LOW,
I have two bedrooms and a shared bath that are on one circuit. Through some initial remodeling/updating, all of the outlets were replaced (3-prong), and all of the light switches. All is fine in bedroom 1 (outlets work, light works)