Nice summary, you put in a lot of effort!
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In the endgame, the enemy King can rarely be mated in the middle of the board. You almost always want to chase it to one of the four sides, or to a corner.
The Staircase maneuver is the easiest way to make use of a lopsided material count such as two Queens vs. lone King, Queen and Rook vs. lone King, or two Rooks vs. lone King.
The Box is a technique that enables you to limit the enemy King's space. As you shrink the Box, you force his King to eventually retreat to the side of the board, where you will finally be able to make it.
If you are left with King and Queen vs. lone King, or King and Rook vs. lone King, you can't mate with the major piece alone. You will need to use both your major piece and King to finish the enemy off.
Watch out for stalemates! There is nothing worse than setting your opponent up for the killing blow, then botching the whole thing to a draw by overlooking that you've stalemated his King! In situations where stalemates might be possible (i.e., the King has limited squares to move to), always take a moment before moving and ask, ''When I play this move, I will his King have a legal square to go to?''
LINK: https://www.youtube.com/watch?v=pFQIhst87lA&t=3s