As they were married in Newcastle registry office I don't know the religion. Their daughter my grandmother Sarah was married in All Saints church, Newcastle which is an elliptical church,and old catholic is mentioned. Fanny is stated as a spinster on the marriage certificate so fanny Willis is a different person. I know she was remarried to a Thomas Quinn. I'm trying to find out about the family in Amargh and when they left thank you
Elliptical (meaning oval) is the style of the church and nothing to do with religion.
It wasn't uncommon, or illegal, for people to use different surnames at different periods in their life. The fact remains that the GRO records the children's mother as WILLIS not Anderson (see replies #7 & #9) so it's likely she used both surnames for whatever reason.
When she married the 2nd time to Thomas Quinn what's listed for her father's name and occupation?