See: "How can you re-wire a wall switch that controls an outlet to control a ceiling fan?" (Follow the link below.) The procedure is the same whether the new device is a light fixture or a ceiling fan.
Yes
To the black wire on the fixture.
Sure. For a light you need a fixture to hold the light and the light itself. The light needs to be connected to a voltage supply which you can get from the outlet. In the outlet box you will have a black, white and bare ground wire. Essentially you connect the white and bare wires directly to the light and switch the black wire (hot) through a switch.
Based on your description it is very likely that either the red wire or black wire is switched and the other is on all the time. In most cases the light of the fan, if it has a light, is connected to the switched wire and the fan is connected to the unswitched wire. This allows you to turn off the light while allowing the fan to remain running. There is no way to know without testing which wire is switched. The white wire is the neutral, connected to the white, or neutral, or common conductor of the fixture. There should also be a bare or green wire in the box to connect to the ground wire of the fixture.
You can make music come on with a light switch the same way you can make a light bulb come on - plug a radio into the switched outlet.
Yes you just have to "steal" power from the switch. Do this by running a pigtail wire from the hot of the switch to the hot wire of the plug. Make sure you do this before the switch or you will end up with your outlet being switched as well.
Most switched outlets have one half that's hot all the time. If that's the case it will be as easy as changeing the outlet. In the center of each side of the outlet there is a small piece of copper connecting the two screws. Look and see if the copper piece is broken on the hot side, if it is then replace the outlet using the constant hot. Cap off the unused wire from the switch. If both sides of the outlet are switched then you can remove the two wires from the switch and tie them together. then either replace the switch and have a dummy or put on a blank cover. You should be all set.
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Disconnect the circuit breaker or fuse to that outlet. Then disable or replace the outlet. This is fairly easy and you can buy a new outlet at a home improvement store for a couple of bucks. If you are not comfortable working with these sorts of things call an electrician.
very easy just pull your self a line from the outlet to the location you want to have the pull light fixture installed ,then connect the black wire to the black wire in the outlet white to the white and the copper ground to the ground then on the other end of the wire at the light fixture location connect the black to the copper screw and the white to the silver screw .and that should make it work with pull string .but make sure the circuit is turned off for that outlet location before you do the instillation
You can if you have a neutral wire present. If the existing switch is what is called a "switch loop" then you can not change the existing switch to a switched outlet. You can identify a switch loop by looking at the wires coming into the switch bow. If there are only one set of wires usually a black and white and they go directly to the switch then you have a switch loop
You don't.