I'd say you have electrical fault in the warning lights circuit.
First thing to do is disconnect the
oil pressure switch and see if the
oil pressure lamp is then NOT illuminated with the key on.
That story your mechanic talks about with your tooth belt belt drive is rubbish.
The belt should never be slack enough to allow it to slip.
Your belt needs to be a bit tighter than what you have, but I don't think it is the cause of your trouble.
Gary