FP3+ Touch screen goes haywire when charging via mains, eventually stops charging and screen stops working

Yes that wasn’t going to work well as the phone and the chargers negotiate at what voltage/power for the charger to apply and as Apple and Qualcomm use different languages it may not work well but may charge at a low rate.

The USB 2 or 3 defines the power at 5V that can be drawn via the USB A socket in a computer. Look inside the USB A socket it will be either black (version 2) or blue (version 3) Either way will not supply what Fairphone/Qualcomm define as Quick charging yet like above could charge at a slow rate.

Howvere you say you have both a cable and charger supplied by Fairphone and none of the other issues really matter if you use those as a pair.
I the Fairphone charger and able don’t work then as you say it seems the phone maybe an issue. Can you use the Fairphone charger and cable to charge another Android phone ? or anything.

If it’s down to the phone it could be the USB port, it could be dirty with dampnes or dust.

Another thing is to dismantle the phone to check a few things. Just the act of dismantling and reassembling may fix the problem as the Faiphone being modular can suffer form poor conatcs between the modules.

Dismantling will enable to ensure the contacts look clean and you can also check for damp ingress vis two indicators.

If the indicators are white and the phone is less than two years old you can contact Fairphine support for a query under warranty.

This post shows the white indicators the main one can be seen once the screen has been removed

and

For disassembly see the Fairphone tutorial on removing the screen