You need help.
2) NO. 20 amps is 20 amps. If the circuit is 240 volts, as opposed to 120, the breaker is 2 poles ( 2 switches) but 20 is 20......and that would not be big enough for most AC.
3) You have to get an electrician to look at the specs and the install manual for your air conditioner, determine what circuit breaker size is required, and the NEC will tell him what size wire to use, based on the amps and the distance.
A fused, or non-fused, disconnect, is a very common and necessary item for an AC install. Even HD would have one. Keep in mind that your local building code may require you to install a 120 volt service outlet adjacent to the outside unit.
How old is the inside coil? When is was installed, was it known that the outside unit would be 13/14 SEER? If not, you CANNOT use it. Also, the GSC 14 is available in R-22 and R-410 versions. Which is yours? Is the indoor coil rated for the refrigerant system you will be using?