Shortest path, nodes on any shortest path, and can Alice evade Bob

You get an undirected, unweighted graph with n nodes. Alice starts at node a and wants to reach node t.

1. Return the length of the shortest path from a to t.
2. Return every node that lies on at least one shortest path from a to t.
3. Bob is also on the graph and tries to catch Alice. Decide whether Alice can reach t without Bob getting to her first.