Translation:The majority of the people believe that I am crazy.
I didn't say you can't say it, I just said it doesn't sound as good in this sentence. Its use in the example you gave is because it's a cliche, and it also has parallelism with the "of the" in some of the time.
Again, it's perfectly acceptable to say "most of the people," but when you're using a computer program that has to have every one of the possible answers input by the staff, you're probably better off using the more common/closer translation.
We're not dealing with a machine translation system here. There is a database of sentences for each question and the sentences are thought up by the authors of the question and then additional ones are suggest by the users by using the report button and "my answer should be accepted" This is what you should do also, when you think your answer should be accepted.
I said that as well. Sometimes I smooth out the literal translations and it judges those wrong so I try to err on the literal side. I also try to imagine a situation where that particular literal variant would convey some subtle meaning, say you'd just walked off the stage after giving a presentation about a perpetual motion machine to an audience and your hermano asks you how it went. You would, in that case, answer "(sigh) Most of the people think I'm mad." When "the people" is a specific group in a specific place, not all people in general, the literal translation is more correct. It's certainly a more common phrase than "You can take the chain to the hotel," or even "bear aganst horse." ;-)
That's actually incorrect. In English, "majority" can be singular or plural depending on the context. In this case, since it is referring to a group of individuals, it is plural. A further explanation can be found at this site: http://public.wsu.edu/~brians/errors/majority.html
Those are technically the right definitions, but it's not really so black and white. Creer and pensar are actually interchangeable in most cases when using "think" to denote what your opinion is or what you believe to be the case (just as "believe" and "think" can sometimes be interchangeable in English as well). I think John is at home = Creo que John está en casa = Pienso que John está en casa. But I believe "creo que" is actually the more common construction here.
However, pensar is always used to denote reflecting or "thinking about something" as in Pienso en mi padre = I'm thinking about my father.