Before upgrading my service to 200A, I had the same setup, minus the central A/C. I charged at night at 24A for almost 2 years before the service upgrade. My nighttime load without charging is a couple of amps. I set the car to charge at 11pm. Occasionally the car would start before a load of laundry finished, but I was still well under the limits of the 100A service
You definitely have a main breaker somewhere, you just haven't found it. Maybe at the meter? You can't leave the main service feeders unprotected. I have a single 200A breaker at the meter, with a "main lug" 200A panel. "Main lug panel" = no main breaker in the panel (think a sub panel with the breaker upstream), vs "Main breaker panel" = panel with a main breaker.
Yes, I'm not sure if its required in the latest code, but it seems to be getting more popular to place the main breaker outside near the meter, presumably so that firefighters can flip the switch as soon as they arrive and not worry about any electrical issues in the house.