Just to add to some of these things with my experience of British schooling from a slightly different area (I've been all over the country and had some interesting experiences):
While lots of Catholic schools are public, lots of CofE schools are state schools and so don't really care if you're of the correct religion or not. In fact many state schools are CofE by default but no one makes a big deal out of it except you're supposed to say prayers and sung hymns in assembly.
Some school will have a Year R or reception which starts from 4, this is a sort of transition between pre-school and school, and they're often only half days to get kids used to being in school and in uniform, and often have 2 different starting points, one in September and one around February/March depending on when your birthday is.
Going out of fashion now, but this also can be to be separated into Infant and Junior schools. Infant from Year R/1 to Year 2 and then Junior school for Year 3-6, sometimes in Primary schools the split is still there but referred to as upper and lower school. You also see the upper and lower school split in High school with Years 7-9 as the lower school, then in Year 9 you take options (which varies by recent curriculum changes but is usually something like Maths, Science (combined or specialised) computers, PE/Gym and English, and then 2 or 3 other subjects, some schools insist you take a language some don't) which you'll then spend the next few years studying for your GCSEs or you can do vocational courses. Years 10 and 11 are usually upper school. Some schools they mix, some they stay apart.
Some schools do this off the bat based on your SATs results in Year 6. Some bigger Primary schools also do this. SATs are based on number levels on Maths English and Science, I don't mind saying I got two 5s and 4 in my Y6 SATs, but because of a snaffoo with my dad he told the school I had two 4s and a 3 (I moved right before starting Y7), so I was in Middle Set for Maths and Science and Bottom Set for English, putting my in Middle Set overall. Because the school ran its core subjects, English Maths and Science at the same time for all three sets, you could move between them in your core subjects, but not the "less important" subjects. Tying into houses, this school was a larger one so ran 2 sets at any given time, splitting us into North and South houses, so you'd have North Top and South Top, you'd have gym with your entire house in your year. (My other high school did the pointless houses thing, we're in the Potteries, so ofc we got potters like Wedgewood and Doulton)
Some schools are just very small. I've been to 2 school with less than 50 children total. I was the only person in my year at one of them, and only 4 of us at the other. You'd often have everyone in one class room, sometimes 2. Often the split was between upper and lower school per class room. Other school are just stupid big. But the average in my experience, is between 25-30 kids per class and 3-6 sets per year.
Sports are just not a big deal. The most common club in my experience is the Netball Club (something Americans do not get apparently), Football Club and Cross Country Club, some schools also have a Swimming Club, if they have their own pool. But very rarely will these be treated as big deals. You might get to have local tournaments with a few other schools, but generally, if you expect to get somewhere in sports, it's not through your school it's through local clubs outside of school. The school will take credit, of course, but you're not going to get scouted or seen by anyone or get into a good university or something like the because of your school club. No one cares. I know quite a few really good athletes from my school days (Premier League goalies, Wold Champion gymnasts, triple jumpers and swimmers who compete for England) none of them got there because of school clubs. In fact most were noticed by high level scouts well before the schools noticed.
