If you are asked to write a proposal, write it like a newspaper article. Tell what, where, when, how, why, how much, etc. The more information you can put into your proposal, the more attractive you should look like an applicant. If you can include specifics about where you want to go, where you will live while there, how you will conduct your research/studies, who in your host country will help you in your endeavor, what other resources will be available to you while you're there, how much you expect the endeavor to cost, what your itinerary will look like, how you expect your experience will enhance your life, etc., you will be viewed as a much more serious candidate than someone who simply says: "I'd like to go to Germany because I've studied some German, I'm of German origin, and I think it would be really fulfilling to live there for a year. This would really help me figure out what I want to do next with my life."
If you are asked to write about yourself, a "personal statement", this is your opportunity to be a little more "creative" than you might be in the other essays. The most important point here is to make yourself stand out, make yourself interesting, and talk about the experiences you have had that have led you to this place in your life where you have this burning desire to do whatever it is you're proposing.
Note: It can be particularly useful, while writing and revising these essays, to work with the faculty members working in the Center for Writing, Learning, and Teaching, and professors you have asked to write letters for you, or who have been asked by the Fellowships office to assist you.