If a visitor reads a website and picks up the phone is this not classed as an online conversion???
No. That is not a conversion, it is a lead. It is only a conversion when it turns into cash, and when a visitor picks up the phone they aren't paying anything.
How you handle that call, how you deal with the customer, how you talk, sell yourself and communicate yourself & your services and products, how you follow up, turn that lead into cash, and that is a conversion.
As regards asking you to "sort out" my website. I think that you'll find that you failed to "convert", because I definitely don't remember paying you any cash.