No; Most high schools provide college coursework or Advanced Placement classes, etc... but they expect the student to pay for the cost of the college credit or the AP exam. If you receive free lunch or discounted lunch then you may qualify to take these classes at no cost. In my personal experience, my AP exams cost around $80 and the college courses were $180 plus the cost of whatever textbook that is being used throughout the course.
It depends on the school and the teacher, but even in college, unless you did so badly in all your classes that you flunked out, they allow you to retake classes so that you can do better and master the subject.
The Quarter and the Semester are different. During the standard school year from about September to about May, there are two Semesters but there are three Quarters. Classes given by colleges that use the Quarter system run for fewer weeks than classes given on the Semester system, but more classes are taken during an academic year.
Taking classes at another school is what most people just call it. Liberal arts colleges call it "an exchange program" (spending a semester at a different college-taking classes, but sill enrolled at your original school) or a college consortium (can take a variety of classes at numerous colleges within the area).
High school level classes to prepare for college
1 Quarter is 9 weeks. So the second quarter of school starts October 17.
I am not clear if you are asking about a college math class or high school math class. If it is college you take it for one semester. Some math classes are divided into two parts and you take one the first semester and then the second half the next semester. If this is high school it could be for the entire year.
This depends on what classes your school is offering and what school you go to.
A short semester offers classes in 4 or 8 week segments and meets for a longer time frame
LPN classes must be taken at a college or university. LVN classes can be taken at a vocational school.
A semesteris a half-year term in a school or college.
Um, I'm not sure what you mean. If you mean a school year, it depends on the school/collece, but usually starts around Augustand goes through the summer until the next year starts in the fall. If you mean a specific college's schedule for a year or a semester, you'll have to look that up on the specific college's site. They will have the deadlines for application, the dates that classes start, major vacation dates, and dates for classes ending, etc. for each semester... or at least the ones coming up relatively soon.
Depending on the school you choose tuition will be about $2500 per semester.