For the first question: AE is a key since AE -> D, i.e., if you know A and E you also know D; since you know D, you also know B (D -> B), and finally, since you know A and B you also know C (AB -> C). Hence, if you know A and E you know all other attributes, hence, AE is a key.
For the second question, you can use the same technique to show that ABD is a key. To show that AB is not a key you apply the same technique and discover that you cannot infer a certain attribute (D).
For the third question, if you know A, D and E then you also know B (D -> B) and since you know A and B you also know C.