Are William and Kate and the Archbishop of Cantebury all Catholic?
No, they are all Anglican - the Church of England.
Prince William would not be able to inherit the throne, although he would still have the title of 'Prince William of Wales.' Prince Harry would become the king after Prince Charles. :-) However, if William and Kate do not raise their kids Catholic, then their kids would still be in line to the succession of the throne.
I assume you are referring to William and kate. They were married at Westminister Abbey, in central London. Westminister Abbey is one of the oldest Anglican Churches. By British law, the monarchy has to be of Anglican faith which includes Prince William. That was the reason for the Archbishop of Canterbury officiating.