So we recently remodeled the ground level floor of our split level home... Ok, remodeled is a stretch, we put up a wall and painted to separate it into it's own 'media room'...

My problem is, at the top of the stairs is a light switch that controls three ceiling lights... now with the wall up, two of those lights are in the hallway outside the room and one is on the inside... I'd like to take that one light on the inside of the room and wire it individually... to a separate switch, a switch inside the media room...

CAN I, just pull that one fixture down, disconnect the wire from that light... cut it, wrap it in electrical tape, leaving it in the ceiling and run a new wire to a new switch... or do I have to take the whole string of lights down and disconnect the wire from the source?

Is it a bad idea to, even thought it'll be wrapped, have a live wire in the ceiling not connected to anything?

Depends how it is wired. We can't guess. May be able to install a switch loop but without knowing where the power starts and ends it's just a guess. BTW, just cutting the wire, wrapping it and putting it in the ceiling is a code violation. Must be in an accessible junction box unless you can pull the wire from the last fixture. Put it in a junction box, wire nut the wires and put a cover on the box.