Smallest total weight in weighted directed graph
4 is the correct one!, because all edges have the same weight, so you need to find the node traversing the minimum quantity of edges.
1 Is wrong because depth-first search doesn't consider edge weights, so any node could be reached first
There is question from one Quiz that I don't fully understand:
Suppose you have a weighted directed graph and want to find a path between nodes A and B with the smallest total weight. Select the most accurate statement:

If some edges have negative weights, depth-first search finds a correct solution.
If all edges have weight 2, depth-first search guarantees that the first path found to be is the shortest path.
If some edges have negative weights, breadth-first search finds a correct solution.
If all edges have weight 2, breadth-first search guarantees that the first path found to be is the shortest path.

Am I right that #1 is correct?