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Water pump is behind the timing cover. Not a easy job.
You need to find the exact place where it's leaking. Your fan was on because the engine was overheating and it was doing what it's programmed to do when the engine coolant temp is too high... To keep running for a couple minutes after the car is shut off.
If I had to take a guess with out phisically having a look,. I'd say it might be one of the turbo coolant lines (if your Engine is the turbo one) , or maybe the radiator.
Under Which part of the engine is the coolant leak ?
Front, passenger side, driver side, between engine and firewall ??