Does the question "which" must always have choices? When is it wrong to use it?

Yes, it does must, or as we say in English, it does, or it must.

In your second and third sentences, "what" is "preferable" to "which." "Which" is used when the choice is limited to a known group of items, which can be implied, like the presidents, or stated, if you listed a group of words or cheeses.

They all look right, to me.

The only use of "which" I can think of that would not necessarily indicate choice might be: "I could do this, in which case I would need to be paid for the services". But, even in this instance it suggests another "choice" in which the person would not be paid. So, this does suggest choices.

Not always. Sometimes it means "pick one" or "identify one," as in the examples you've given. When used in statements, it can mean something specific. For example, I have misplaced the book which you gave me.