In the sentences: "Pourquoi parle-t-elle?", "Qu'a-t-elle?" what does the "-t-" stands for?
You can't have two vowels beside one another. Not that they fight with each other, but it sounds weird trying to enunciate parle-elle. So, add a -t- in between, and the vowels get along.
You just encountered one of the grammatical tricks of French called the liaison. In these 2 sentences, the "-t-" stands for nothings. It is only present to facilitate the pronunciation of two consecutives words, the first one ending by a spoken vowel and the second one starting by a spoken vowel. It would just be awkward to tell those sentences without the "-t-". It is usual to encounter this type of structure in the interrogative form when you switch the pronoun and the verb. Remember than unlike English, in French we tend to pronunce much more the vowels (with a few exceptions).