@CDOESenior2k16 answered the first part of your question. With regards to graduate level classes. I imagine most undergraduate student’s do not take one grad level course during their 4 years of college. That’s because between Harvard’s General Education requirements (http://www.generaleducation.fas.harvard.edu/icb/icb.do), foreign language requirements, expository writing requirement and concentration requirements, there just isn’t enough time to schedule those grad level courses, that require undergrads to have taken all the prerequisites for those courses. For example, a 400 level grade course is going to require a student to have taken the 100 level intro course and two additional level course at the 200 and 300 level before being allowed to take the next level course,
My guess is that it’s not normal, that the majority of Harvard students do not cross register for even one class at MIT during their 4 years of college. One reason is scheduling. College classes are often scheduled in blocks of time with 10 minutes between meeting times. However, it often takes about 20-30 minutes to get to MIT from Harvard and another 20-30 minutes to return. So, taking a class at MIT involves extra commuting time making it impossible to take back-to-back classes. And in the winter, it’s a long hard slog to MIT from Harvard yard.
Classes at Harvard usually have several components. A lecture, which is always taught by a Harvard professor and a section, which is basically a review of the material presented in the lecture, which is taught/lead by a TA/TF who in most cases is a graduate student. In addition to the lecture and section, science courses have lab’s that are also taught by TF/TA’s.
All Harvard professors are required to have office hours, so student’s can drop in and ask questions. A professor isn’t going to seek out a student and force them to attend office hours, but if a student makes the effort and reaches out to a professor, that professor is accessible and willing to help.
Student’s interested in walking on to a sport first need to complete the NCCA Eligibity Center registration: http://web3.ncaa.org/ECWR2/NCAA_EMS/NCAA.jsp. Then, they need to be good enough to compete at a D1 level.
FWIW: I don’t know anyone who has walked-on to Harvard’s soccer team, but I know a student’s who walked-on to Harvard’s baseball team. I imagine it’s the same deal with soccer. Harvard’s coaches are more committed to their recruited players than their walk-ons because the recruited students could have gone elsewhere to play ball . . . and may do so if not given the playing time they were promised. Consequently, while a walk-on practices with the team, they spend most of their time on the bench, and get to play in a few games where the score doesn’t matter.