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" Personally, I never exchange pieces unless it is absolutely necessary, because I suck at playing king and pawn endgames (and because I think a lot of exchanges are pointless)."
If I win just one minor or major piece, I will always look for ways to force trades (simplification) to a very easy to win King and Rook vs. King endgame. This is how most of my games are won, either by resignation because my opponent is down one or two pieces, or by check mating the enemy king with my king and rook. I know this endgame far better than any king and pawn vs. king endgame, as I believe it is the easiest endgame to learn.
Silman's Complete Endgame Course, from beginner to master, by Jeremy Silman, is probably the best book on endgames on the planet, for everyone except maybe those that need something harder... to reach IM or GM.
His book is organized by rating (Part One/Endgames for Beginners - Unrated to 999). Part Three (Class D 1200 to 1399) is much harder, for me. I am happy to go over just part one and part two from time to time.
So, king and pawn endings require much more study than king and rook vs. king endgames.
Below is a game where I was happy to force a trade of queens (39.Qa4+ Ke5 40.QxQf4+ KxQf4) with a tactic (skewer) to simplify the position to a king and rook vs. king endgame. There were a few pawns left on the board, but that is usually not a problem when I am the one with the only rook on the board.
Here is an example of a simple K+R vs. K endgame.
That book is not free you have to pay :(
Oops, sorry, didn't realize you have to be a "premium member" to download it, but you can read it there online, the diagrams aren't very good but the content looks intact.
Don't overvalue space advantage. It's not the space that counts but the position within the space.
When the position looks quiet (there are no tactics that you can find), you could start looking for imbalances like weak squares, outposts (for your Knight), (semi) open files. Based on these imbalances, try to come up with a plan. For instance, if you see that your opponent has a backward pawn on a semi open file. Try to find the most efficient way to target that pawn. Which piece should go where? Based on that you can start playing moves in a structured manner, even in quiet positions. And if the situation on the board changes (e.g. the backward pawn is well protected), evaluate the position again and come up with a new plan.
It's not the number of pieces that count, it's the number of ACTIVE pieces that counts! How many times have we never got around to moving our rook at a1 until the end of the game?
That depends on your opening and the variation you play.
Availabe at Amazon? How many pages?