The relay is tripped by the ECU completing the earth connection, the black and red would suggest this wire is the switched (ignition) live feed to the relay, there will be another +12V feed which is the actual feed to the pump.

So by what you have found, the problem is after the relay, how did you run the power to the pump, onto the original pump live, or a independent connection, if the latter it's most likely the original live to the pump that is at fault.

Yes your problem is caused by excessive current hence why the fuse is blowing so almost certainly a short. It's almost impossible to connect the connections to the wrong terminal, there should be 3 on the negative. The heavy duty black and two browns with ring connectors.

Martin