Use GFI breaker for charging?

With a Tesla Wall Charger no, as it has built in GFCI protection. Other brands may or may not. Read the friendly manual.

Definately do not install yourself. Hire an electrician.

The instructions with the charger should specify

As an electrical contractor and a city inspector and plans examiner I recommend you or your hired professional meets minimum standards. National Electrical Code 2020 says "210.8(F) Outdoor Outlets. All outdoor outlets for dwellings, other than those covered in 210.8(A)(3), Exception to (3), that are supplied by single-phase branch circuits rated 150 volts to ground or less, 50 amperes or less, shall have ground-fault circuit-interrupter protection for personnel. " ground-fault circuit-interrupter protection for personnel - a safety device designed to protect people by cutting power when it detects a current leakage to ground between 4 and 6 milliamperes  Tesla wall connector provides class b which is a specialized ground-fault circuit interrupter designed to trip at a threshold of 20 milliamperes (mA) or higher 20mA won't kill an adult but may kill a child/baby

Honestly, you need to get an electrician to help you. There’s things you can do like mounting the charger and running the wires but please get an electrician to check your work and install the breaker at a minimum. You’re dealing with too much continuous power that will be used day after day to mess this up. There are torque specs for all the terminal screws and breaker that you really need to follow.

GFCIs may cause problems with the wall and mobile connector (even though they’re have different types of fault safety devices), but GFCI may be required for outdoor outlets. Because the GFCI (and especially arc fault) breakers are so expensive I would just use a GFCI outlet ($25). If it causes trouble then you can ditch the GFCI and have an electrician install a low cost wall connector there that has GFCI built in.

many thanks

In most cases don’t and it’s advised to not use GFI. When you do you’ll trip 100% of the time at some point in your charge session. In the week i was waiting for my wall connector i got so annoyed i ripped the GFI breaker out of my garage and put a standard one in temporarily. I reverted it back when i wired the wall connector. But if you are not skilled or comfortable with electrical work please hire a professional.

Have GFCI wall outlet. It has started tripping several times a month now so would not recommend GFCI outlet paired with mobile charger which has built in GFCI Talk with electrician. This conflicts with NEC code 625.54, which requires GFCI protection for EV receptacles, but Tesla’s built-in protection satisfies this safety requirement.