Not really. Some service centers/stores have wall connectors (which are L2) in public parking spaces, but they aren't generally promoted.
These are what (L2) wall connectors look like:
https://www.tesla.com/home-charging
These are what (L3) superchargers look like:
https://www.tesla.com/supercharger
No, that's L3 (supercharging).
L1 - feeding the car 120V AC wall current. Onboard charger converts AC to DC to charge the battery. 2kW max (16 amps @ 120V AC).
L2 - feeding the car 240V AC wall current. Onboard charger converts AC to DC to charge the battery. 11kW max for current Teslas (48 amps @ 240V AC)
L3 - feeding the car high voltage DC current (350-400V or more, depending on the car's make/model), directly into the battery, bypassing the onboard chargers completely. Power levels limited by car, battery temp and state of charge, and power of charging station. Teslas can draw up to 250kW max for short periods (~700 amps @ 350V DC). Also called DC fast charging ("DCFC")
There are 3 main types of L3 charging - Tesla Superchargers (aka "NACS", 72kW, 150kW, 250kW max depending on station design), CCS (European and other US car companies), and Chademo (Nissan, Mitsubishi). North America is transitioning to Tesla/NACS (CCS/Chademo dying off here). Europe uses CCS. Japan uses Chademo.
You're probably talking about L2 free chargers, so probably yes. Anything less than 15-20kW would be L2. The max possible L2 charge rate in the spec is 22kW (80A @ 277V), but few cars can draw that much (first gen Model S, F-150 Lightning). Most public L2's (Chargepoint, etc) are 6-7kW (30 amps at 208V or 240V)