Questions related to semidirect-product of Klein four group?

Question

I have four questions related to Klein four group. and I know the answer two of them. ( the first two) and I want to know answer

1. Does $V_4$ has an automorphism of order 6?
2. What are the orders of automorphisms of $V_4$?
3. Can there be a non-commutative semi-direct product of $V_4\rtimes \mathbb{Z}/5 \mathbb{Z}$
4. Can there be a non-commutative semi-direct product of $V_4\rtimes \mathbb{Z}/3 \mathbb{Z}$?

The answer of the first two is well-know, $Aut(V_4)\simeq S_3$ so we can answer question number two from the answer of number one. so I have trouble with the last two questions. and is there is a way I can use the answer of the first of two question in the answer. since all these questions is one part problem. any help appreciated.