Check pressure cutout switch on low line line (smaller of the two a.c. lines).
If the pressures are always equal running, the compressor is bad and would need replaced
No, if you mix them they will form a gel and ruin the compressor. You will have to have the system evacuated and replaced with the new refrigerant.
More than likely you need to have your refrigerant recharged. or your A/C Compressor needs to be replaced.
does the fan work? is the system charged with the refrigerant?
Your 1992 Lincoln Town Car takes 2.5 pounds of R-12 refrigerant or 2.75 pounds R-134 (if system converted)
Refrigerant level low or cooling fan not working. worst case would be that the compressor no longer can build enough pressure and needs to be replaced
The ac system will have to be drained of freon and the pressure released. Then the compressor can be removed and replaced. Replace all o rings along the way as well.
The system will need to be drained of Freon and pressure. Then the lines can be removed and the compressor replaced. Change all o rings during the procedure.
Possibly a low refrigerant charge
No harm will come from driving it. You just don't want to use the AC system without any refrigerant in it - that could harm the compressor. The refrigerant also cycles the compressor oil, so running the compressor without the refrigerant in it is detrimental in this regard. Also, since you had to open up your AC system to replace the compressor, you should have also replaced either the receiver-drier or the accumulator (your vehicle will be equipped with one or the other, depending on whether you have a Thermal Expansion Valve system or Fixed Orifice Tube system - it'll never have both), as they contain a desiccant which will become fully saturated within five minutes of exposure to atmospheric air. The desiccant in these components is vital to the proper operation of the AC system.
Make sure that there is power getting to the ac clutch when the switch is jumped. If the power is there then the clutch is bad and needs to be replaced.
Doesn't matter - if you open up the compressor, you open up the AC system. By law, this must be done by an ASE certified technician in an EPA approved shop with the proper equipment to evacuate and store the refrigerant. This prevents refrigerant from being released into the atmosphere. Whenever the AC system is opened up, the receiver-drier (if it's a Thermal Expansion Valve system) or accumulator (if it's a Fixed Orifice Tube system) must also be replaced.