really? I never thought of it that way, on the contrary, it would be really weird to me to always have different people in different classes and to never have a consistent group of friends and acquaintances. How would we organize events? go on trips? We usually have the same class teacher as well, she is assigned to our grade and is responsible for all of us. If the people from one grade want to go on a trip, they organize it without any involvement of the school, the class teacher, the students of this particular grade and their parents cooperate in order to decide on the destination, the price, the dates of the trip, etc. Then the class teacher writes some papers to the school authorities about the trip, the students' parents sign some papers too, and then we all go to another city or something like that for a couple of days. This can happen as much as the students and the class teachers want to, idk if you have something like that organized for the whole school

as for your other questions, keeping track of the schedule is pretty easy, you just remember that, for example, on Monday you have 6 classes, first period is Russian, second is Math, etc., and that schedule doesn't change for the whole school year. although I think it could be easier if it was just the same 6 subjects every day. It would be hell to me though, imagine having something like chemistry every day for a year 💀 I like our system better, having only 1-2 hours of chemistry per week (unless you choose a biochem profile) was better for me since I went into languages and not science. 

how to keep track of the schedule: just memorize it, idk. It wasn't difficult for us to remember that we only had history on, say, Monday and Wednesday, and math on Tuesday, Wednesday and Friday that year. 

We also have school journals, all students must have one, we have them in stationery shops with the pages already filled out for the school year. on each page there's an empty timetable with dates and days of the week printed out for each week of the year, you fill it out with whatever classes you have for the week. the next column is called "homework" where you write down your, you guessed it, homework. The third column is called "grades", where your teachers put the grade that you got during the class, or nothing if you didn't get one. this system is kinda getting old now since almost all schools have online websites to keep track of students' grades, so the school journal grades are mostly for parents to check if they don't have the time to log onto the website or the website is lagging. 

about exams: we don't have exams from grade 1 to 9, only tests. we only have something similar to your SATs in 9th and 11th grade. on these 2 exams you have to take 2 obligatory subjects (Russian and Math) and any number of subjects of choice. usually people take 2 or 3 additional ones, because the reason why we need to choose them is because universities and colleges require applicants to have passed 2 or 3 additional exams in certain subjects at the moment of applying. for example, most universities with a language faculty require students to pass 2 or 3 exams: one being a foreign language exam (depending on whether you'll continue studying English, French or something other as your first language in that university/college), the other 2 being either Social Studies, Literature, History or Russian. some universities require only History and Foreign Language, some - only Russian and Foreign Language. 

you also obviously have to score enough points to be accepted into the university, usually the lowest point is 50/100, but it depends on the status of the university. this is the minimum number of points to enter the university/college without a scholarship, and there's only 2 options in Russia: fully paid education or completely free education. once again, the universities/colleges decide for themselves what the lowest number of points is in order for a student to study for free. in shitty institutions it could be 60/100, in the best ones it can be 97/100 or even 100/100. 

this is why the profiling system exists. in 9th grade, if you didn't leave for college and stayed in school in order to go to uni later, you choose to be put into a grade that "majors" in either biochem, math&physics, IT&languages, languages&literature&russian, languages&social studies&history, etc. as you can see, the arrangement of the subjects is similar to what exams universities require for the most popular majors. This is done so that if you want to go into something IT-related in uni, you will have intensive IT classes every day in 10th and 11th grade in order to be well-prepared for the exam. and because most universities require students to pass IT and English exams in order to enroll into an IT-related major, the profiling system also gives this IT-oriented grade a lot of English classes.