- Who Shakespeare is?
As far as I can think, that is not a grammatically correct sentence. I am not a grammar expert so I am wary of making a definitive judgement, but to my native-speaking ears it sounds very wrong. Even if it is possible to contrive a scenario where it is grammatically valid, it is not something you would commonly hear.
Can the second sentence be said in situations like in a classroom for, instance, when the lecturer says, "Let me tell you who Shakespeare is"?
Yes, the lecturer's sentence there is fine. But you are not using "the second sentence". You are constructing a new sentence which also uses the words but "who Shakespeare is". That doesn't mean the words "who Shakespeake is" form a correct sentence in isolation.
Or, can it be a heading on the slide show:
Yes, this works as well. But again, in this example, "Who Shakespeare is:" is not serving as a sentence in itself. It requires completion from the subsequent bullet points to form a grammatically complete and correct sentence.
Also, in both of these examples, the words "who Shakespeare is" are used to form statement sentences, not interrogative sentences.
So, the short answer is:
(That is, when do we use No.2?)