Please tell me what it could be.

Check for a bad ground circuit for the PCM and sensors.
Are there any trouble codes?

Are there any trouble codes? Most parts store provides free scanning services.

No sparks are usually caused by a nad crank position sensor, behind the timing belt, inside the cover.

P0108 = MAP sensor circuit high voltage input. This fault could be the cause of the difficult or non starting etc.

However you have been pulling sensors etc so this could be a false alarm. You would need to reset the computer and try starting to see if any codes are triggerred. You would need prolonged cranking time to trigger codes.

As to P0420, with a cleaned out catalytic converter, this code would be present after every 2 starts. There is nothing you can do about it except treplace the catalytic converter.

Have the alternator checked/tested. Seems it is overcharging causing the problem.

Hopefully that solves the problem and thanks for the donation.

Have a great weekend.

Voltage regulator is inbuilt and since you can't have engine running with it connected, you would need to remove it for a bench test.

P0116 is a fault with the Engine Coolant Temperature switch. This can cause difficut starting and stalling when engine is warmed up.

P1399 is temporary codes for misfiring.

Others have been explained to you.

Have the ECT checked.

It is possible bench test don't tell if it is overcharging and yes, you are correct about the PCM controlling the charging. Apart from the alternator, the PCM can also possibly cause charging faults.

One way of finding out is to replace with a known good alternator and test. A no charging problem is not too bad but an overcharging system is very dangerous as it can take out a lot of electrical components when voltages spikes.

I once had an older model vehicle which had every bulb in the vehicle blown and wasted a lot of time diagnosing as I did not think of all bulbs blowing when lightings did not work.