Ok, look:
Я получил три с минусом is used almost as often as Я получил тройку с минусом but the 1st sentence is shorter than 2nd so it's easy to say it. It depends on your preferences. Кол is more colloquial than единица and it's used in spoken language.
Now something about our school system. The school year consist of 4 quarters. During the quarter(четверть) a teacher gives homeworks and then corrects it,ask questions in the class, gives tests, calls kids to blackboard where they make some tests. The teacher gives grades for homeworks on kids notebooks and its can be 1(for nothing) 2, 3-,3,4-,4... and the like. The grades for tests teacher gives on so called классный журнал - class journal(?). The grades also can be there like 1,2,3-,3.... and so on. But in the end of a quarter the teacher counts the final grade and gives it on a report card. For example if a kid got 3,3-,2,4,4,5 the final grade is 3, or if a kid got 4,4,5,5,5 the final grade is 5. It is like an arithmetic average of all grades with round-up. Also, in the end of a school year a teacher counts all quarter grades and gives a final grade for the year by the same rules on a report card.
The 1 is the worst grade and it means that a schoolkid knows absolutly nothing about subject and I've never met anybody who got it for all tests, homeworks and teacher's qeestions only 1, so this grade never gives on a report card. The 2 means that a kid at least knows what is a teacher name and he was at some lessons. Three "2" and more in a report card means that a kid keeps down next year.
Надеюсь, я понятно объяснил?