You are correct and answered all of your own questions. The tank bladder is shot. The tank needs to be replaced. As far as the copper, do what is easiestwhile still maintaining solid connections. If you have to sawzall the thing off, do it and replace the fittings as necessary.
General Rule of Thumb: The tank should have an air pressure 2lbs below the cut -in setting, so if you have a 30-50 psi pressure switch, fill the tank to 28lbs. This, of course, is static pressure, meaning the system is shut off and all water relieved of the system.