How can you stop water leaking through the shower head when cold water or both hot and cold water is on?

Be aware that for the first few minutes after turning off you will get the shower head leak a little. This is because the shower head has a large cavity inside that fills up with water in use. When you turn off, that water has to go somewhere, so it dribbles through the outlets of the shower head.

If both shower heads are off no water should be going to your shower head. the only thing it could be is your shower valve itself. you probably have a pinhole in one of your o rings on the valve stem. try replacing the valve stems.

I would start by replacing all the washers and o-rings on the hot and cold valves ( a lot cheaper than replacing the entire valve stem ).

Try replacing the Valves, and then the pipe holders, (for want of a better Word) to the wall.

The shower diverter has a bad seal - very easy to replace.