Re: Adding alternator wires. Big-3
The only wires that should be on the positive battery terminal is the cable going to the switch and a wire to the bilge pump if you have an automatic bilge pump. Everything else should be at the output of the switch or a terminal block.
The output of your alternator should not be connected directly to the battery, It should also be at the output of the switch or connected at the starter. That way, if you alternator shorted to ground for some reason, turning the switch off disconnects power to it.
Your new battery also needs a switch for its loads. That is why I recommend the switch by Blue Seas. It is basically 2 switches inside so you only have to turn one knob.
The one cable with the insulation exposed is not marine cable. It almost looks like house wiring cable because the strands are so big. I would replace that cable immediately before it breaks. Whoever did the wiring of the boat before you did not know what he was doing.