Does “free school” in the British education system mean exactly that — free of cost? If so — gee, no wonder non-Catholics go for it. Regardless, American Catholic schools (that I’m familiar with) are essentially the same way insofar as pupil population is concerned. If you can pay the tuition, they don’t really care what you believe. Schools attached to a particular parish may have “in parish” and “out of parish” rates, but that’s it.
Yes. 'Free schools' became part of the education system in England and Wales in 2010. They can, in some ways, be considered similar to charter schools in the US (where those exist). In England and Wales, they are taxpayer funded - one of six different types of tax payer funded school. The system allows 'faith schools' to be funded - in a technical sense, all schools could be considered faith schools (all schools are supposed to include an 'act of worship' at assemblies but it's well known that many schools no longer follow that rule) with the state religion - Church of England - being the default, but other faiths can start schools on the same terms.