I have a Tesla home charger and wanted to avoid adding another 240 charger to the garage. I experienced the same problem you describe in your photos, and returned it. I bought the Tesla to 1772 adapter from TeslaTap and it has worked perfectly, every time. I highly recommend you take a look at their product.
I do not have a home Tesla charger. I would be using the Tesla adapter for public charging only. Can you tell me (us) if the Teslatap Mini works at public charging stations?
The Tesla Charger at home looks and feels like the destination Charger. If there is a difference I am not aware of what it would be. They both deliver 240 AC to the car charger which then converts to DC.
This is very different from the Super Charger of course which is delivering DC directly to Tesla-Only vehicles.
What I am certain of is that I had the same issues you presented both on the Charger (Red) and the Fault indications on the Jeep when using the Lectron, and once I returned it and bought the TeslaTap it worked fine.