If you wish to control the second head from the original shower control, then come off the head. That way both shower heads can be controlled from one location. Realize that the water pressure will decrease as they have a common source, which is normally a 1/2 inch line.
Buy to shower valves and install them so they are on opposite side walls or if you have a existing shower with one valve then the easiest way is to take out your old shower head and replace it by buying a chrome wye fitting that with two chrome nipples you can install to shower heads another way is by buying 3 chrome nipples and one chrome T and two chrome male by female IPS 90 and thread them into the the T and then you have room for two shower heads and they can be put side by side. The best way is to have two shower valves & shower heads, depending on your water supply and how you run your water pipes to the valves, most likely you will increase your water flow if not almost double and make sure you have at least a 2" drain & trap.
As long as you are using the same size supply line there shouldn't be any difference.
Electricity and water don't mix. You should not have a socket in the shower.
Toilets, a water supply and a shower block.
If you wish to install 2 batteries and keep the same 12 volt supply then connect them in Parallel. You will double the capacity (Amp Hours) but still have 12 volts. Click the link to see a parallel connection.
All showers need valves. They can be for the water supply, balancing the water and control of the shower. Without the valves, your shower will leak, causing damage to the surrounding areas.
Supply and installation about -600.
Run a new cold supply line from the source. This will drain less pressure from the the cold shower line.
Shut off the water supply for starters
Usually the power supply.