(a) Yes. (b) No.
(a) Yes to both in some countries.
However the tax is usually charged to people who attend church (see Wikipedia for a list). On the other side where churches can’t or don’t charge taxes some countries make churches as charitable organizations exempt from tax. And concurrent with that donations to the church can be used as deductions or credits from personal tax.
Further, some countries allow special deductions or credits for religious leaders. In Canada, most churches are registered as Charities which exempts them from taxes but also limits their spending to certain activities and can tax their income generation if it is an active business.