It sounds like two different problems: the motor running backwards because the ESC to motor wiring got mixed up, and the beeps because the ESC to timer wiring got mixed up, or something broke. Did you maybe unplug things in a hurry when you got the reverse running? Could you have plugged them back in wrong?
To fix the motor-backwards issue, you need to reverse any two wires from motor to ESC.
To fix the always-beeping, you need to carefully check that the ESC is plugged in correctly, and that no wires are broken. If you have any RC gear, you can connect the ESC up to the throttle channel of a receiver and see if it responds correctly to the throttle stick on the transmitter -- if it does, then you know the problem is with the ESC, if it doesn't then things are still up in the air, but point more toward the ESC end than the timer end.