At most colleges and universities, students can graduate with Latin honors. Cum laude, Summa cum laude, and Magna cum laude are the honors distinction.

It's an entirely separate program (extra units, extra difficult classes); not as easy as latin honors (cum laude, etc.).

It all depends on the college and whether or not they grant Latin honors.

No, except at the beginning of a sentence because it is

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"With" in latin, is cum, as in magna cum laude: "with" highest honors. That's why a C with a line over it, denotes the latin translation.