Might just be me but I would expect a COLD water tap to run with cold water – now I may be wrong on this but it seems correct to me!!!!!!!!
Get an electrician to test your immersion heating elements from your description I suspect you have a blown water heating element.
As for the switch you found making a wirring noise – I beleive this is a “red herring” to the fact.
Get it tested out by a competent sparkie.
Selgas Services Ltd
Craftsman Gasfitters, Plumbers, Electrical Service Technicians