Our twins took MAP tests for the first time last year - they were 6th graders. They took the tests on a computer - I believe they are multiple choice. (It might be worth checking the internet for sample questions.) I imagine they are always computer based, as they are "adaptive" tests, meaning that the level of the questions are selected in real time based on performance on earlier questions. The computer keeps feeding questions until the software is satisfied that a stable score has been established. I believe this means that there would be effectively no ceiling for even a very advanced six year old.

We did not get "official" results from the school until a couple of months after the testing, but eventually figured out that at the end of each test, the computer displayed the score so the student could see it. So if I knew they were going to be tested on a certain day and reminded them that morning to take note of the score, I could get the scores on the same day.