How should I start and close the letter.
Presumably not "Dear Sir"
Do I still use "yours faithfully"?
Your salutation will depend on what church this is.
For a Catholic priest or an Orthodox priest: Dear Father ....... [nb the Orthodox Churches have a very complicated system, but this is a sensible approach]
For an Anglican priest: either Dear Mr ........ or Dear Rev. .........
For a non-conformist (Methodist, Baptist, Presbyterian etc): Dear Mr ......
If you are addressing them by name, you end "Yours sincerely".