Catchment is meaningless. Many of those faith schools require a form that has been signed by the church confirming you're a regular attender, which is why many churches resemble a playgroup on Sundays as parents suddenly find religion for the necessary time (differs by school/church - some demand 2 years attendance!) to get the all-important signature.
So you can move there but you may also have to attend.
If it's one of the schools that doesn't require attendance and a signed form - there's still a few left - places are given out based on siblings, needs and distance, so the 'catchment' is only as far as the number of places. One year they might allocate all 30 kids within 200 yards of the door, the next it might be 150 yards, the next 450. Depends how many kids apply and where they live. But like I say, if it requires attendance, then the kids with perfect church attendance records are allocated places before the atheist kids on distance.
(of the 8 faith schools in my area, they are so oversubscribed with 90 applications for the 30 spots, that all the places were given to church-attendees.)
OK, next topic - the religious character of a school differs by school. All schools in the UK - fun fact - are required to do 'daily worship', and that's even the non-religious schools. Some take this very seriously and some don't, but it's up to the school. Some Catholic schools can be very hard-line pro-life/abstinence-only, some are not. It really depends on the school itself. One of our CofE high schools got into trouble for an anti-abortion lecture too, but then over the road the Catholic school has major discipline issues. So, yeah, it really depends on the school.
What you want to do is just visit the schools. Check your council website and see which of them demand church-attendance proof. Decide how you feel about that. I didn't even consider them - I outright refuse to a) lie for a school place and b) believe the religious discrimination in our school system is wrong. Children should not find it harder to get school places due to their parents' beliefs. Now you'll be left with schools with no attached church, and schools that may have St Something in the name but don't demand attendance. Visit, ask questions, see how you feel.