It's not a silly question at all.
No, you needn't articles in become Prime Minister, king, queen, chaiman etc if there's only one position in those cicumstances. But become a teacher, assistant, minister etc - there are a lot of them; smb becomes one of them.
Don't we have to put "the" or "a" infront of Prime Minister, Superman like a doctor?
Sorry if its a silly question.
Articles are tough to learn.
1. In that case, you can use an article or not. Without the article, it is a title; with the article it is a position.
2. That should be "What does it take..." No article here, because Superman is a person (sort of).
3. That is not a sentence. It could be the title of an essay or something like that. The real question is "How does one (or do you) become a doctor?
This needs an article because it is a profession/job.