New Goodman condenser unit run almost contiously using too much e

If the unit is running in cold weather than there is ice building up on the coils located outside. This is normal in that the unit is running in heat pump mode heating inside and cooling outside, After the unit detects the ice build up it briefly reverses the cycle heating the outside coils melting(defrosting) the ice which you observe as water on the pad.

The video gives you an example of the defrost cycle!
2012 Trane XL15i Heat Pump Defrost Cycle Steam Show

Your 3 phase unit should not have a capacitor. I'm guessing it's single phase. If it's a single capacitor than the compressor should not be going to it also. To test the motor, common to start plus common to run should equal the ohms you get between start and run. For instance, 1.2 ohms+ 2.2 ohms= 3.4 ohms. Follow the wiring diagram on the inside of the door, send model number!!

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This is true as long as it is not a heat pump. Make sure they replace the piston (metering device to match the outdoor units required piston size. Or if the indoor coil is metered via TXV, it will automatically meter the refrigerant flow. If you are mismatching a system, make sure an acid test is performed on the old refrigerant and take appropriate measures with the new system if the test shows positive acid. They need to definitely install a liquid line drier.

The capacitor starts the motor. You would have had some other problem had the motor not started. The A/C ran until the failing capacitor no longer provided the ability to start the motor at which point your A/C died.
My A/C bulged both its capacitors 2+yrs ago and it's been running ever since they were replaced, no problem.
I think you're OK.

If you had sparks in your breaker box then you need to call an electrician to look into that. If the a/c is blowing the breaker you may have a shorted compressor and will have to replace it or the whole condensing unit, depends on the price of the compressor vs a new condenser.

first off you should have a four ton unit. what is your super heat? is it pulling attic or outside air?

they would need to change the coil indoors to a 3 ton. If the blower speed can be increased it should be fine.

First of all, clean your outside coils so that you are assured of good cooling air. The compressors have an overtemp device that is usually internal to protect them against heat. If you have an air compressor use it to blow out the coils good. If the compressor will start, the capacitor is good so it sounds like a cooling problem with the compressor

at 5 yr on goodman unit rhe comp should of been under warrenty if theat is what was bad with it on the rudd that was a 3.5 ton out door unit are you sure the pump is bad pulling locked rotar amps or shorted to ground check the wires on the comp to make sure not burnt check the capicitor as far as replacement i always lean twoards new unit unless not going to live there long due to comp is 1 yr and labor around 850 +325 for pump i would go with another used unit over comp replacement 13 seer goodman w 99yr pump and latley have 5 yr free labor and I normally dont recommend a brand of unit on this site go to a hvac store and ask who may have a used unit I have had some still w warrenty before that came from remodel jobs in up scale areas! if helpfull rate me good luck

The high side/low side pressure equalization you describe is normal for a compressor sitting idle.

If you have an ohm meter you can check the compressor windings for opens and shorts. If your compressor is 3 phase as you state (this would be very unusual for a residential unit) you should have continuity across all 3 phases and no continuity to ground. Take the compressor out of the circuit before you check.

If the compressor does have crankcase heat, it should have been left on for at least 24 hours before starting the unit. Another cause for failure could be overcharging which could have resulted in refrigerant slugging back to the compressor.

Does the unit have any low or high pressure control safeties? If so, check them too - some have resets. You said the condenser fan ran so it's not likely the breaker blew, but check anyway and also check to make sure you have available power on all 3 phases.