Two questions about data structure here

1.The minimum spanning tree of a connected weighted graph with vertex set V={ A, B, C, D, E } and weight set W={ 1, 3, 2, 5, 1, 7, 9, 8, 4} must be unique.

Is this correct, why or why not?

2.

For a directed graph, comparing to the representation of the adjacency lists, the adjacency matrix representation is easier to:

A.do DFS

B.find the in-degree of a vertex

C.do BFS

D.find the vertices that are adjacent from a vertex I need full explanation for both, thanks