I am going to install a new ceiling fan with a built in light over an existing light fixture. The ceiling fan will have a remote control.

The issue I am concerned with is that there is a row of three separate lights in the room, all three of which are operated together (all on or all off) by a single wall switch. I will be placing the fan over one of these lights.

I want to be able to run the fan without having the room lights on. Does the wall switch to the lights have to be on for the fan to work? Or is there a live wire which will provide current with the wall light switch off? I could then turn the fan on and off with the remote without having the other lights on.

I don't know, is there? Have you looked?

Pull the switch plate off and shine a flashlight in it. If you have one pair of wires with the black and white both connected to the switch, it is a switch loop. There will be an always hot wire at one of the lights, chances are, the one closest to the breaker box.

If you have 2 pairs of wires, with the whites connected together, and the blacks to the switch, then none of the lights have power unless the switch is on.

Actually, it is common to have an unswitched hot in the ceiling box even if you do not have a switch loop. In many older homes, the wires for the outlets ran through the ceiling boxes.