A battery charger puts out pulsating DC since there are no filter capacitors in them. Seeing AC is normal and lower than expected DC reading is normal, too. The more modern units will have filtering since they have other circuits that need pure DC. When it is on a battery, the battery acts as the filter.
Maybe you have had an old tube type radio that hummed? That is bad filter capacitors that allow the DC to pulsate a bit.
Try it on a battery and it will probably be fine.
The fins on the rectifier diodes are there to get rid of heat. A diode is like a check valve in this application. It only lets current flow in one direction. The center tap on the transformer allows both the positive and negative excursion of the AC to be used.