Something is wrong...

You should not be able to move the fan that easily...
Check to see if they sold you the wrong belt. If the angle the belt is made is not the same as the angle of the pulley then you have real lack of friction problems ( translates to noise ). If the angle is not correct it is almost impossible to get it tight enough to avoid noise....Stranger things have happened ( TO ME ) than a belt being misslabled at the factory (for example)... it will REALLY cause some head scratching...

Another possibility is a bearing going out in the alternator.. I can not think of anything which adding an electrical load would point to the water pump.. unless you are running one of those rare electric water pumps on your car...