What should I write in my essay? Do I need to describe a specific research proposal? How long should it be?

The essay should describe your motivation why you want to come to our institute. You do not have to go far back in your past and motivate your choice from your childhood, but you can motivate it from the interests you developed during your studies and from the courses you took. You do not need to have a concrete research idea, we only want to get an impression of your general interests and motivations. Half a page is usually a good length, and it should certainly not be longer than one page.