Engine check light normally goes out after 3 engine start/run cycles with no fault detected, doesn't really matter how many miles each trip is as long as it gets up to a reasonable operating temperature each time.
You can disconnect the battery for 30 seconds however you will need to re-initialise the sunroof/windows/power hatch. You won't lose radio or sat nav presets though. Whatever app you used to read the codes appears to have a clear codes option at the bottom, that will clear the warning light and easier than disconnecting the battery.
It could of been a temporary glitch but if the warning lights don't go out, or you get the errors again then definitely check the battery -ve connection, and earth straps going to the engine as it really seemed like an electrical issue.
I doubt cleaning the sensor would stop those faults occurring, and the heater errors are essentially unrelated, but it will likely restore some smoother running and better economy if it was very dirty.