This is a subordinate relative clause.
If this is not correct, how should I correct it?
1. That's what's taking so long. (If this is okay, why? 'what's taking so long' is a question?)
In the first place when we want to connect two sentences, we look for a common point in both of them. In this case it is "it". To unite the sentences we use on word which is a pronoun, and is the common point in both parts of the sentence (in this case it is the attribute of the main clause and the subject of the subordinate). Here the pronoun what has been choosen because we really don't have a reference; we don't know what it refers to.
That is it. It is taking so long.
That is what is taking so long.
Therefore it isn't a question because this "wha"t is a pronoun and not an interrogative.