Do all students study all subjects until they leave at the end of 12th grade?
There is a core educational programme which runs through the 12th grade but generally, no. It's not as specialised as A-levels but for example, my school required 4 years of English, 4 years of maths, 2 years of lab science (biology & chemistry) with a further 1 non-lab science (like geology, etc.), 3 years of history/world study and foreign languages were optional. The students who were in advanced or college prep courses would take 4 years of all of those things, students who were looking at trades or military options would not.
Do students choose which classes/subjects to take?
To an extent but it depends on what the school offers.
Do students have a lesson in every subject every day - so first period for one person would be the same subject every day?
Depends on the school. I didn't. Maths and English and history were every day, science and labs less frequent and alternated with music/theatre/art electives.
What is the Honor Roll?
A list of students in the school who have met certain grade criteria. It varies from school to school. In my school one had to receive all As and not more than one B grade to be considered "high honour" and if they had a mix of A and B grades it was considered "honor roll".
I think I understand that AP classes are for bright students and equal college credit?! Do students choose to take these classes or are they selected?
This is correct - AP classes are essentially college-level studies with an exam sat at the end of the year, which, if the student scores high enough, will fulfil the education requirements at a university. I took the English, Maths, History and Chemistry exams. Ostensibly they are open to all as long as there are seats.
Finally, if you graduate from high school is that all at one level? Here in the UK we get exam results for subjects at 16 (GCSE generally) and then at 18 (A level generally).
Yes, it is a general educational requirement which is somewhat higher than a GCSE but not quite an A-level (AP classes are more like A-levels, honestly.) Students graduate at 17-18 so I suppose that makes sense.
Oh final final... do US universities specialise from the beginning or does everyone study more general education in the first year? I taught 4th grade in MA on an exchange and heard talk if ‘remedial classes at college/uni’.
Universities give their intake of freshmen placement tests to see where their academic abilities really fall. The issue with schooling being regionally controlled is a school in one town can vary wildly from schools in other towns and states and so even though you may have passed four years of maths the university needs to see that for themselves...and if you are not up to standard on the placements, they place you in remedial classes to "catch up" -- which are generally not worth college credit.
Universities become specialised much more quickly than a high school curriculum but there is still a general education component to it all -- so despite not being in a scientific discipline, I needed 6 credits (2 classes worth) of maths, sciences, etc. to meet graduation requirements.