Classification would be the best form for essay B.
For essay A, comparing and contracting needs some form of classification i.e. The democratic party does x, y, and z and the republican party does x, y, and z. However, in a compare and contrast essay you are not meant to simply present the information. it is your job as the writer to synthesize the information you are presenting. As in, it is not just that these parties do x, y, and z, but you must make it explicit how x, y, and z are different, the same, or similar. You do not need this second step in a classification essay.
Essay C should be a literary essay. While you could say that the themes in George Orwell's 1984 fall into 3 categories and explain what they categories look like, that does not make for a particularly interesting literary analysis. This essay is not just about what the themes are, but the function and impact they have in the context of the book.
Essay D shouldn't use classification at all. The prompt isn't asking you to make a list, it is asking you to explain a concept or take a position.
While classification could be reasonably used to some degree in essays A and C, the only essay where it is the BEST is essay B. All the prompt asks is for you to list out different web based email programs and describe the features. You are not asked to compare them, take a position on them, or find some deeper societal meaning to them. You are simply asked to describe them. That is why classification would be the best way to organize essay B.