Here are outline solutions for questions 2,5 and 7.
2. If e is not saturated, there is a min cut which does not contain e.
5. Define a bipartite graph G=(A,B,E), where Ai is connected to Bj if they are not disjoint. Find a maximum matching and take an element from each edge (intersection).
7. Similar to what was done in recitation - only here the max flow should be 3|V|.