Yes. MIT and Caltech are notorious for having freshman math and physics classes that go 30 percent faster than corresponding courses at other highly ranked institutions. Sadly, this means that 20% of MIT freshmen do poorly in their freshman math and physics classes, despite being some of the best-prepared college students in the country. MIT's standard freshman physics courses used to have similar rates of Ds and Fs, prior to a major pedagogy change during the first decade of this century.
And no. In California, almost anyone can attend a community college. And either after passing enough remedial classes, or after demonstrating that the remedial classes are not needed, you can take essentially the same calculus classes as are offered by the University of California at Berkeley. If you manage to get in to MIT, you can use those the non-remedial classes to get out of MIT's classes. But because MIT's classes go 30% faster, you will need to have taken 30% more semesters-worth of non-remedial classes at the community college.
Many colleges offer multiple versions of some courses, depending on students' interests and planned majors. These courses can vary widely in difficulty, content, and teaching approach. Some "honors" versions of classes are only offered to students who meet special admissions standards.