Puzzle of the week #5

There are a lot of written rules about strategy and tactics that players of today have to learn in order to improve their play. Some rules are easy to understand and apply, as the chance to try them comes very often. One example is placing a Rook on an open file. Other rules are harder to learn, or easier to forget in the heat of the battle. The art is to continuously analyse our positions and decide which rule is good to follow at any given time. For our puzzle (source unknown) please see diagram.
Black to move and win. Which rule applies here?
Please answer to both questions. This is a 2 points puzzle. The answer will be published next week together with puzzle #6.

Puzzle #04 solution:
White is looking at a very sure loss: the extra pawn seems pointless, the double pawns h5-h6 are the worst possible pair one can have, plus the King cannot catch the g5-pawn. The only thing in favour is Kh8 blocked in the corner. Let's see if we can do something about it. See solution for a complete answer:
[Event "Puzzle #04"][Date "2008.01.31"][Result "1/2-1/2"][SetUp "1"][FEN "7k/5K2/7P/6pP/8/8/8/8 w - - 0 1"]1.Kf6!! {White has to delay getting on the h6-square by a move and then we can have a stalemate} (1.Kg6?? g4 2.h7 g3 3.Kh6 g2 {White loses because it has to move the King}) 1...g4 2.Kg6 g3 (2...Kg8 3.h7+ Kh8 4.Kh6 g3 5.Kg6 g2 6.Kh6 {Draw}) 3.h7 g2 4.Kh6 {Draw}

Correct solutions:
Jacob, John D, Karl, David, Frank, Jeremy, Bryant, Algerd, Matthew - 1.0 point

Standings:
3.0 Bryant, Jacob, Jeremy and Karl
2.5 Matthew, Frank and David
2.0 John D.
1.5 Jakab, Nicholas and Algerd
0.5 Alejandro, Joanne, Vera, Mark, Kenneth, Karen, West and Katerina