Question 3
Finding a Hamiltonian cycle in a graph is as hard as determining the answer to the Marbles Elimination question; i.e, there is a reduction from the problem of Marbles Elimination to the problem of finding a Hamiltonian cycle.
Determining the answer to the Marbles Elimination question is as hard as finding a Hamiltonian cycle in a graph; i.e, there is a reduction from the Hamiltonian cycle problem to the problem of Marbles Elimination.
Marbles Elimination is in P by a reduction to the Max Flow problem.