Why are you NOT using a stat.
Quite clearly if the car is misfiring etc and reading "temp to the sky", it is LYING to you.
If it overheated to this extent you would have after effects.
You may well have two seperate problems, a eager(knackered) fan switch, even new ones can be duff, plus and electrical problem, resulting in LOW voltage, do the wipers/heater blower slow down as low voltage affects dc motors a lot sooner than other items, the tacho and engine running is usually last to go.
I would conect up at least temporarily a VOLTAGE gauge to the car and watch when this goes funny again, the battery will recover a bit and have no problem in a hot climate starting a hot engine, I would also check all earths that you can find.
I would see if the main ecu earth ahs broken inside the insulation, these are earthed on the plenum cover/throttle cable bracket with "O" ring terminals on the end, this is the main earth for the ecu, and it is not unknown foir these to break inside the insulation.
tabetha