the engine cooling fan should cut and in out ? this is normal behavior especially if the car is moving slowly
now if the fan is coming on with a cold engine then thats a different matter and I'd 1st consider replacing the engine coolant sensor and also check the state of the wiring between the sensor and the engine loom - check it for chafe damage and hard sections indicating a short
I'd say as long as the engine isn't overheating then yes you're fine to carry on driving the car
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