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Parking and charging outside of home???

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My understanding was that 40 mA was the limit for EV charging. I don't have the NEC standard (don't live in the USA) so I can't easily check.

The NEC doesn't really list GFCI listing requirements but UL 943 governs them. From NEC:

Class A ground-fault circuit interrupters trip when
the current to ground is 6 mA or higher and
do not trip when the current to ground is less than 4 mA.
For further information, see UL 943, Standard for Ground-
Fault Circuit Interrupters.

The standard for GFCI devices approved for protection against electric personnel shock trip at 5 mA within 25 ms. A GFCI device which protects equipment only (not people) is allowed to trip as high as 30 mA of current; this is known as an Equipment Protective Device (EPD). The NEC calls for personnel shock protection, the 5 mA level.

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Is it possible to have an extension cable to the HPWC one?

No. The HPWC must be hard-wired to a 100A circuit and the 25' cable is the maximum length permitted by NEC article 625. This is also the end that connects to the car, so it cannot be extended without rewiring it onto a longer cable.
 
Hmm. That's unfortunate. On a related question, is there an installation guide somewhere out there about the HPWC? How do I tell if it can be installed in my house at all?

You'll need to either have a friend with reasonable electrical knowledge, or an electrician, to look at your panel and service to see whether you could add an 80A continuous load to your existing electrical infrastructure.