24v feed is the voltage input to the switches........................ reasoning is that [same as with solenoids] we use them for very short duration, so even tho they are 12v rated they can handle the bursts. With use and in s short time of dancing your voltage will drop and so the current will rise. It is current that kills switches/noids/motors so starting with a higher voltage means that you dont get to the point where you go below the rated volts and where the current starts to rise.
and the same, to an extent, answers your second question.
Lesuire batts are good at standing discharge to a very low level
BUT
you wont be running your system batts to a low level as this is the cause of most fires etc... running on too long between charges so the current rises too far. Ideally you want to stop and recharge as soon as your system shows signs of noticeable slowing.
Standard starter batts are good at punching out high cranking amps for a short duration and that is what we need.
Weldability [wwsgroup.co.uk]
you want 70mm cable [p/n EZC70P] and disconnects to suit [p/n EW450/17P and EW450/18S]
there is a diagram in Tony's "wiring help" topic at the moment.