If the pump is in the loft (I’m not familiar with the shower) then a Surrey flange or similar should have been fitted. It could be something as simple as poor pipework Installation.
Yes, you can usually bung it (the cold feed on cold water storage cistern). There’s usually one as a gate valve (not always though) from the cold feed to the cylinder, usually entering the base. Photos of setup?
Why is this?
Are you sure it’s a multimeter? Sounds like a 2 pole voltage indicator. I would rewire the switch with just LNE and connected to the correct terminals