Hi @ItsOnlyATorch lots of people have given helpful answers though there are a few discrepancies. Here is my take on it as a parent of DC with differing school experiences and also a former classroom teacher who has worked in several schools.
GCSE numbers: yes some DC will take a lot fewer or a lot more but most YP in mainstream state secondary will take between 7 and 10 GCSEs. The majority (typically about 60% each year) take 8 or 9.
If DC take fewer than 8 it's usually bc they have some SEN and drop a subject in favour of extra support in say maths and English. If a DC takes more than 10 it's usually bc they are doing an extra as a twilight (lessons after school) such as stats for able maths students, or maybe a home language such as Urdu or Polish.
All DC (pretty much) take maths, Eng lit and lang, science (two or three GCSEs).
Science and how it is taken can vary and can also affect numbers. There is some confusion on the thread but the options are basically “double science” (there is no single science GCSE award now) which is all three sciences but two GCSEs, or “triple science” which is individual GCSEs in biology, chemistry and physics. The advantage of this is that you can get stronger and weaker grades eg 8-7-4 if you are not good at (say) physics. With double you get the grade averaged to (say) 5-6 or 6-6.
Some schools timetable triple as an option in an option block; other like my DCs' school set the students into triple and double, with triple done in the same number of lessons (so speedier, hence DC need to be more able). Those DC will get one more GCSE than the rest of their cohort.
The YP then choose options. Some schools insist on geog or history and an MFL; some insist everyone takes RE GCSE; some ask for one from a specific group; some may group the choices in blocks; some may insist on a creative option (drama, music, art, DT); some may insist on a tech option; some may give a free choice. There may be a choice of 1, 2, 3, or 4. Not often more than 4.
Examples: DS2 did triple science and had to take hist or geog and Spanish; he chose history and then had two more choices (PE and computing) which were just chosen from the list of other options. 10 GCSEs. His sister at the same school also took triple, she had to also take one of MFL, hist, geog, computing. She chose geography and then as her free choices, French, music and drama. 10 GCSEs. A friend's DC at another school had to take double science, geog or hist, French and then had one choice (PE). Total of eight GCSEs. Friend of DD's did double science and had four totally free choices and took (IIRC) drama, dance, art and sociology. Nine GCSEs.
Post 16 - three A levels is all you need for uni; some take four but mostly when one of those is further maths. A level equivalents such as Btecs are available and yes, changing rapidly. Most school sixth forms offer only or mostly A levels; colleges offer a wider range of courses (inc A levels) and often a more relaxed environment (no uniform or dress code, come in only when you have a lesson).
HTH and apols for an essay as usual from me haha.