abltmusician,
Its a good thing you are finding interest in this scholarship so early. As you can see from our experiences, it would really benefit you to start thinking about it.
You said that you are already a graduate student. I think most applicants are using the scholarship as a way to enter graduate school. I'm not sure how that will affect you but I think it will raise some questions.
We all took the Japanese exam. The test are in the exact same format as the ones on studyjapan. This year, and maybe from now on, they used a slightly different format. Instead of 3, one hour, test(A-C, easiest to hardest, i think similar to JLPT lvl 4, 3, & 2 skill level), they gave 1, one hour, test that got progressively harder. I think they eliminated the easiest of the 3 test, A, and started with questions from B and ended with reading from C.
Abdoukun has some good advise. Honestly, I didnt even read the reading. It was a bit long(and hard), and then you only answer 2-3 questions. So I just "tried" to read the first sentence of each paragraph. read the question, tried to find it in the reading, and then take a guess. I think it sort of worked... but I dont even know my score.
I think most of us have never met the professors that we are contacting. Yes, I think it is hard to get a reply from a professor. But with some persistant, I'm sure anyone can get a reply. The best way of doing so is email, it gives you time to write it, it gives them time to reply (and perhaps is the easiest way for them to reject by simply not replying). I personally sent out emails to about 10 professors, got a reply from 4 of them, and 1 of them rejected me. The other 3 expressed some interest.