Short answers, pulled from the story.
Judea Pearl described best-first search as estimating the promise of node n by a heuristic evaluation function. This function depends on the description of n, the goal, information gathered during the search, and extra knowledge about the problem domain.
Greedy best-first search expands nodes using only heuristic values without considering distance from the start. Neither A* nor B* qualifies as greedy best-first search because they include an additional cost factor alongside estimated distances to the goal.
Efficient selection of the current best candidate for extension typically uses a priority queue. The queue orders nodes based on their heuristic distances from the target to allow rapid selection of promising paths during execution.
Best-first algorithms often serve path finding needs within combinatorial search environments and appear frequently in navigation problems inside artificial intelligence systems. Gaming magazines and trade press have documented their use in complex routing scenarios where brute force methods fail.