Are there honor and ap classes at Harvard University?

AP courses are a high school thing, not a college thing. Some colleges have honors programs (which you must be accepted into to take the honors classes), but they do nothing more for your GPA than any other course, and top schools don't have these programs - honors programs are for state schools and similar that want to offer more advanced classes, but most students aren't ready to take them. All the classes offered at top schools are similar to honors courses at lower ranked schools.

Everyone applying to Harvard has the highest grades in the hardest classes and very high test scores, and Harvard turned own more than 94% of these students this year, including thousands of 4.0 students and valedictorians. You need a lot more than that to have a shot at getting in.

AP classes are at a high school level only. You will not find AP level classes at any US university.

Some US universities do have Honors College. It works differently to how honor classes work in HS

Harvard's acceptance rate is under 10%. They get in over 20,000 applications and enroll about 2000 students. You will need to score over a 30 on the ACT or on the SAT 700+ on each subject score-CR, math and writing.

Plan on paying at least $45,000 per year to go there