Charging at home is typically cheaper. Around 1/2 to 1/3 of the cost of a public charger. There are also some free public chargers but they are typically slower charge around 6kW and are limited to an hour or 2.

Depends strongly on the area. I’ve never seen any above 41c/kWh, and one of my local chargers does 13c/kWh after 8pm.