Low to zero pressure on low side test port

EPA regulations: Freon 22 units are no longer available, Units that are compatible are available They come pre charged with nitrogen It must be dumped. If there is freon in the old system it should be pumped down into the condenser unit before the inside unit is removed, Close the high side king valve and run the unit until the low pressure reads near O Close the low pressure king valve. and turn unit off. 410A freon units are readily available. Most if not all 2 ton air handlers will work with any outside 2 ton unit though some building codes will not allow a mix. Their reason: if something fails who is to blame:

First you need to determine if it is a heat pump or straight cool condenser. The reason is the low voltage wiring is different. This is the correct way to install an outside unit.
1.Pad must be level and unit should be secured to withstand 140 mile uplift wind with tie down straps.
2. Make sure breaker size does not exceed max per data sticker on unit. The electrical whip should also be correct wiring size for breaker AMPS.
3. Remove the shard er core valve to prevent damage to it, protect king valve with wet cloth or thermal trap paste to avoid damage. Connect the liquid line small cooper pipe to unit by brazing. Then run through gauges Nitrogen at low psi to prevent shoot build up in line set, now start brazing the suction line large cooper pipe, once finished help cool with water cloth.Check visually for any missed spots and re braze. Once you are comfortable that braze is a good seal now it it pressure test time.
4. (The above procedure is assuming that the inside unit has already been installed correctly, including the line set to unit.)
Through gauges connect Nitrogen compressed gas tank and increase psi in the line set to 350 psi and let stand ten minutes. If pressure is still 350 on both gauges you have a good seal, release the nitrogen into the air and remove tank from hose. Once gauges read 0 psi on both sides high and low you can start the vacuum process. These pressures can differ per refrigerant ( R410A example).
5. Hook up the Vacuum pump to the middle hose from gauges making sure you have replaced the shard er core valve back into the ports.tighten all hoses to any connection on machine, gauges, and pump open gauges and turn on pump allow to run at lest 20 minutes or until you reach 100 microns in a vacuum.Shut, close gauges and shut off pump remove the hose from pump.connect this hose to refrigerant tank and purge to center hose at gauges ( minus) amount of purge.
6. Now you can open the king valve and let refrigerant flow out of the condenser into the line set and air handler otherwise you have to add the refrigerant, newer refrigerant has to be charged into unit in the liquid state not gas state. R410A older refrigerant can be charged in gas state R22.
7. Hook up electrical,breaker off check with volt meter, follow diagram on unit. Then hook up low voltage, for straight cool depends on t-stat and unit witch colors they use follow schematics. I have found that Goodman use blue as common and yellow for cool, make sure that the same colors are used in the air handler to provide the 24 volts to outside contact coil.
If this seams difficult, well it is unless you have the correct training incorrectly done can cause damage to unit and to personal health ..
8. Or call a professional HVAC tech.

i would check fan speed. it's probably on high. you might be moving more air with new system. a dirty evaporater on old unit woud have gave you a larger temperture drop.

No reset button. As for low/high pressure switches they reset on their own when the problem is corrected. Usually low refrigerant.

i would suspect the valve on suction side not open. if the other system failed on a burn out you could have a blocked dryer or orfice at coil.

low air flow or low on refrigerant.

The service valves are closed. Therfore once you solder to the stubs on the valves your gauges will read what is in the line set and evaporator coil. Pressure test to 150 and let sit. If determined your pressures held then evacuate with vacuum pump. You are evacuating the line set and evap coil only because your service valves are closed. THIS IS THE PROPER WAY TO DO THIS. Once evacuated to 500 microns, close manifold and open valves. You will then see your refrigerant charge and determine if more refrigerant is needed. Good Luck !!

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You can install another 3 ton heat pump any brand or you can use a regular condensing unit and put a heater in the air handler.

Only 2 wires going outside.
Yellow from the thermostat and the common wire from the lv side of the transformer.

It looks like you did make some improvements when you replaced the coil and metering devise. The fact that this system never ran right "out of the box" is suspicious. My first instinct is that the system is either unmatched in size or the whole system is sized incorrectly. Do your Heat gain/Loss calcs and see if it matches close to what is in there, both for the coil and condenser. Secondly double check that the evap you installed is matched the same as the condenser. In some situations the ID coil can be over sized by a 1/2 ton. But that is the only exception and it does not apply to all cases.

If the system is sized and matched correctly, then I would consider the compressor to be the problem.