"Tomorrow's class is at five o'clock."

Ders = course (as a unit), lesson, lecture, class
Sınıf = classroom, section of a class, the people in the classroom.
Kurs = course that doesn't belong to the regular education system. ie. Language courses, driving courses; school that offer such courses

'-ki' is an affix that doesn't follow any vowel harmony, so it's the same for every word (except for the exceptions 'dünkü' and 'bugünkü', of course).

Nope! "saat" always comes first.

As a side note, "saat" is also a bit irregular and would take i/e endings for suffixes (saatte)