Need your help, please. I have a single pole switch that controls the wall’s receptacles. It has one 14/2 cable, white/black/ground, where the white is hot. I would like to install a ceiling fan. I expanded the box for the second switch and ran a wire for the fan. My question is, can I use a power source from an existing wire?
No. You do not have the required conductors at the box. It sounds like you simply have a switch loop, where one conductor is ungrounded (hot), and the other is an ungrounded switched conductor. To power a ceiling fan, you'll also need a grounded (neutral) conductor.
If you could pull an additional conductor (or cable) from the power source of the receptacles, you would be able to do what you want. However, as it currently stands, you're short a conductor.