Answer the following questions explaining your reasoning briefly but precisely.

1. Why any node in OPEN with f(n) < f^*(n) (the cost of the optimal solution path) will eventually be selected for expansion by A*?
2. Is it true that all admissible heuristics are equal in the sense that A* will search the states in the same order no matter what the heuristic is?
3. Is Breadth-First search complete if the state space has infinite depth but a finite branching factor?
4. Does the fact that A* is ``optimally efficient'' mean that A* will never expand more nodes than any other algorithm?