Learn English – a day in the week called

In the United States, one term is suitcase student, and an institution which has many such students may be known as a suitcase school. For example, consider this 2013 New York Times article about Central Connecticut State University. Connecticut is one of the smallest states, and CCSU is an institution sponsored by the state government, so the great majority of its students are from areas less than two hours away (which is extremely close by US standards), and so this pattern is prevalent.

Almost half of Central’s 7,700 full-time undergraduates live in dorms or near campus. But most vanish each Friday, joining the army of undergraduates at “suitcase schools” around the country who desert their campuses on weekends.

They head home for the same reasons suitcase students always have: favorite meals, moms (and now dads) still willing to do their laundry, high school friends and sweethearts, and jobs. The refrain “There’s nothing to do on campus” is self-fulfilling. …

^{Moore, Abigail Sullivan. "Off Off Off Campus" in The New York Times, Jan. 31, 2013}

The article is full of other suitcase terms, including suitcase culture, suitcase mentality, suitcase legacy. It refers to a student for whom life at the university residence halls is temporary, not a true home; therefore, they pack a suitcase of clothes, as if going on a vacation somewhere.

I wouldn't consider this term to be commonly used, as most colleges and universities are either traditional residential institutions or commuter schools, where only a very few students or none at all live independently on or near the university campus. Surprisingly, I found no results for it in COCA. In Google Books, however, they go back to at least the mid-20th century, e.g.

One problem that is bothersome today is the "suitcase student," who leaves campus on Friday afternoon and returns on Monday morning. ^{Treudley, Mary Bosworth. Prelude to the Future: The First Hundred Years of Hiram College. Association Press, 1950}

Ole Miss remained a pleasant headquarters but scarcely a community of scholars. It was, as the expression went, "a suitcase school." ^{Lord, Walter. The past that would not die. Harper & Row, 1965}

You are talking about a transcript.

Although, I honestly have never received a "paper" with my college grades. Usually, if you are dealing with institutions like school or jobs, you will have to ask for an "official transcript". This is usually a sealed hard copy to prevent tampering. But nowadays, everything is electronic, so I don't think students usually handle a transcript themselves. The school or some online services will handle the official transcript for you. If you are allowed to view your transcript online and print a copy yourself, that copy is usually referred to as an "unofficial transcript".

In high school, or earlier, I remember receiving a paper. This was called a report card. There was also an official transcript, but that too was handled by the administration. You could also ask for an unofficial copy or an official copy.