1. A directed graph can have cycle only when it has back edge in DFS tree. So it is FALSE.
2. The distance between two vertices may be same using the different paths. Also, no of edges in those paths may vary. So this statement is also FALSE.
3. BFS distance from source is the minimum number of edges to reach the target node. In DFS, the depth of any node will surely be greater than or equal to minimum number of edges from the source. Hence, this statement is TRUE.