Yes to all this. It is fundamentally the responsibility of the student to keep on top of the various application components and deadlines for each school. Obviously the more schools a student applies to, the more difficult this can be.
Additionally, some schools allow a grace period for non-student controlled materials, while some do not…this is another aspect that a student has to understand for each school on their list.
Michigan is an example of a school where all application components must be received by the deadline of the round the student is applying. For example, if the teacher LoR comes in after the EA deadline the app is rolled to RD.