What is important in the endgame besides centralization and activity? I'm a little confused about this. I know pawn structure and centralization of the king is essential in the endgame and I also know that activity, especially from the rooks is very important. Playing with little space also seems to create far too much tactical problems, although it often seems playable according to computer engines that I use to look at the match after it's over (playable not very pleasant to play with so little space). However, it seems that there is not much strategy beyond trying to be the one with the superior minor piece or superior rook or superior king and the better structure and going after the square and pawn weakness.

I know there's some endings with mating attacks against the king, but this usually requires rook on the 7th/2nd, at least two pieces, a safe king (to prevent forks and a perpetual check), and a weak opposing king. Sacrifices might not necessarily be required, but often are. These conditions are a bit hard to get even against players that are not very good. I suppose all these advantages for a mating attack on the end would have to be forced in the middle game.

So, I know the strategy and some cool tactics can also revolve around passed pawns and piece imbalances or space (lack of space) and I also know there's some interesting piece sacrifices, like those you do with exchanging a minor piece for 2 pawns but you get to lock all the opponent's pieces and kill counterplay. Zugzwang is also pretty cool. But still, maybe I'm just not very good at positional sacrifices and tactics to try to make things more interesting, however it seems to me that it is very hard to materialize a win in very balanced endings, even against some poor, but not so poor players. So, there's more to endings that I don't know? Maybe trying to force complex theoretical endings could make things more interesting? (Not sure if I would know how to do that and even so my opponent can just know the solution for such theoretical ending too?). 

Anyway, another point is about king safety. With one rook and 3 minor pieces on both sides around I'm usually scared of king centralization, while with one rook and 2 minor pieces around on both sides I'm usually in doubt of whether I should centralize my king or not. Any easy tips to assess the safety of a king which is not on the first rank? Also, I was watching a blitz match between Hikaru and another GM and I noticed really a lot of pawn pushs, knight moves, just some rook moves and even fewer king moves by both sides, maybe they were just trying to do fast chess and that's the strategy somehow, but it made me really curious. Finally, can you quickly think in situations where the endgame king is more needed in the flank than in the centre? Situations where it is not so obvious why, like passed pawns running to queen.
Your question meanders a lot, but I think what you are asking is, “What factors other than king centralization and piece activity are crucial to the endgame?”

I have highlighted three areas below in bold that not more important than the other areas discussed, but just that they are not often discussed, so you can take note of them.

You hit on a lot of them in your question, so I may reiterate some of them here. The first thing is that endgames, despite their simplicity, require an incredible amount of calculation. They tend to be very specific in nature, and often we see that moving a piece to a specific but seemingly equal square, often a rook, is the difference between winning, drawing, or even losing. There are A LOT of mistakes made in endgames, even by the greatest of players. So, in essence, your comment about there not being much strategy is both true, and not true. You must keep the strategic things below in mind, but ultimately, as in much of chess, it comes down to brute-force calculation.

Ultimately, you are not going to get a set of catch-all rules for the endgame, but I will compile a list of things that you need to think about, but only endgame study and experience will allow you to prioritize them for any specific position you may end up having so you can, hopefully, calculate the proper course you should take. I will say that focusing on this area of the game, and taking many opponents into the endgame by trading, you will win a lot of points. I have only recently started to go to local clubs again after many years, and I have been playing a lot of 1800-2000 players in blitz, and while I often beat them like a drum in the middlegame, occasionally, they manage to stay equal until the endgame, but only then, they make mistakes and lose equal endgames. Being a bit older now, I can say that while I overlook things in the middlegame, and even hang material from time to time, I do not recall any of them ever outplaying me in an endgame and actually winning.

One thing that you touched upon that is SO important, that I feel compelled to discuss, is how much of higher-level chess is about trading off your bad pieces for your opponent’s good pieces. This is in the opening, middlegame, and endgame. Entire plans are often based on this key point, and games are frequently decided by this one factor. Listening to GM Peter Svider’s broadcasts on chess24.com, he often discusses this specific to a position in passing. It is like a masterclass listening to him, in general, so I cannot recommend it enough.

So, here is as complete a list of endgame factors to consider as I can compile.


You must know basic theoretical endgames. The book “100 Endgames You Must Know: Vital Lessons for Every Chess Player” by GM Jesus de la Villa, and its companion workbook, are highly recommended for this aspect. Since we are all looking for positions that are familiar to us, you will be aiming for positions in this book most of the time, whether as the player, who is trying to win, or the player, who is trying to hold the game and draw. Knowing some of the famous drawing positions like your opponent having a bishop and rook-pawn, but the bishop does not control the queening square (obviously with your king able to get to the queening square) are critical to good endgame play. Or, knowing that you can still draw in some queen versus lone pawn positions if the pawn is a bishop- or rook-pawn on the 7th with your king nearby is another example.
Planning: Be prepared to plan strategically based on the factors that follow below. If the position is quiet, you will simply have to decide where you want your pieces, and how to get them there in the best manner. This planning starts in the middlegame, and thinking about active transitions into the endgame.
Extra material, whether an extra pawn, or trying to convert an exchange (for example, knowing that rook and pawns versus knight and pawn endings are often some of the easiest to win).
You have probably heard this a million times, but when up in material, trade pieces, not pawns as the pawn’s value increases when there is less material on the board.
Conversely, if you are behind, you want to trade pawns in the hope that it will leave your opponent with a single pawn that will be impossible to promote, or maybe that you can sacrifice a lone remaining minor piece for it, leaving an immediate drawn ending.
Strange material imbalances. Sometimes, and this is always scary, is a piece for three connected passers. This is a VERY general rule, but knowing that if the three passers are at 3rd, 4th, and 5th rank is usually a draw, but further back, they are a loss (assuming other material still on the board for the side with the piece), and on the 4th, 5th and 6th, often a win.
King Position, often centralization, but also the ability to shoulder the other king out (that means to keep the king from approaching, or forcing him to take a longer route so you gain a tempo or two), or is the king cut off (often in rook endings), or even the ability to go where the other king cannot follow because he would be going outside the square. For example, just yesterday, Smirnov resigned to Anton Guijarro because he could go wide, and Smirnov could not stop him by following since h5 would win. 
The opposition in pawn endings.
Piece activity, and as you said, often rooks (on the 7th), but a bad bishop is another common example of a piece that can have limited activity, especially when tied down to defending its own pawns. This can often lead to the closely-related zugzwang, a frequent visitor in bad-bishop endings.
Weak squares: Just because the middlegame has passed, that does not mean that you cannot still think about weak squares. The famous Cohn-Rubenstein, St. Petersburg 1909, endgame comes to mind. Rubinstein made a beeline to the weak square h3, and then advanced his kingside pawns, leaving him with the better, and winning, king position.
Pawn structure: This includes protected passed pawns, damaged structures, the ability to create a passed pawn, especially an outside passed pawn, and pawn islands. Are all the pawns on one side of the board, making it more likely the game will be draw? Corollary to my last sentence: Knowing that the structure f2-g3-h4 makes it hard for the opponent to make a passed pawn, even when down 4-3 pawns all on that same side, thus this is often desirable.
Advanced pawns and the threat of promotion (or actual promotion), both for queening directly, but also for just tying down the opposing side, and keeping them busy. Having an advanced pawn when down a pawn, or even more material, can also be an equalizing factor since it forces the opponent to be tied down to prevent the pawn from queening.
The ability, even at the cost of a pawn sacrifice, to create two passed pawns that are far separated, often in opposite colored bishop endings. In Topalov-Shirov, Linares 1998, Shirov uncorked one of the greatest moves in chess history, 47…Bh3!!, with the sole goal of creating passed pawns so far apart that Topalov’s bishop could not deal with them.
Unbalanced pawns when up a pawn: This is a very crucial topic, and one that is not often discussed. If you have an extra pawn, such as 2 to one for your opponent to 3 to one for you, you have the opportunity to create two passed pawns to your opponent’s one passed pawn. This strength is amplified if they are connected. This factor, which happens in rook endgames frequently, can make an endgame a lot worse than it otherwise might appear material-wise.
Tactics: There are more tactics in endgames than most people realize, but they mostly do not make it into most tactics books since they are more bare-bones tactics. When an endgame position is very complex, you cannot use basic principles, and you must calculate the same way you would a complex middlegame position. Coincidentally, right now, I am reading the only book I know of that is dedicated to endgame tactics, “Van Perlo's Endgame Tactics: A Comprehensive Guide to the Sunny Side of Chess Endgames”.  This book, in its fourth edition, is a labor of love, and covers tactical areas including pawn breakthroughs, zugzwang motifs, bare-bones mating attacks, and stalemate tricks among others. I highly recommend it.
The drawing tendencies of rook endgames. There is an old Savielly Tartakower (sometimes attributed to Tarrasch) saying that “all rook endgames are drawn”. Obviously, that is not true, but it is just an exaggeration about their drawing tendencies, and you need to keep that in mind when trying to win or draw.
Opposite-colored bishops, and their drawing tendencies. In opposite-colored bishop endings, the stronger side still wants to put their pawns on the opposite color of their bishop, but the weaker side may actually want to put their pawns on the same color as their bishop since it can be defended so easily now.
Bad bishops (opposing either a good bishop or a good knight). Try to avoid placing pawns on the same color as your bishop at all costs if your opponent has a same-colored bishop as you, or a knight.
Good knights in blocked positions (often opposing a bad bishop).
Bad knights (they do not defend well against rook pawns).
Having two bishops in the endgame is often a decisive factor.
Fortresses. We often see this in opposite-colored bishop endings, but there are many in other endgames too.
Another thing that I see a lot: Players, who are winning a close ending, but they take the time to hunt an extra pawn, when they could be taking that time to push their own pawns that much further. I mostly see this in rook endings. Sure, take the extra pawn if it is a direct part of your plan, or it is getting in the way of a direct part of your plan, or because it is actually dangerous to you; but otherwise think first about pushing your pawn(s). Imagine how many pawns you will be able to take later if you are up a piece. You may not get the chance if you went pawn hunting for the sake of pawn hunting.
The famous Shereshevsky quote: “Do not hurry”. Often an endgame is drawn, but you can lull your opponent into making a mistake by entering a position that looks similar to one that you have previous had during the game, but there is a small difference. Your opponent loses their sense of danger, and you pounce. Of course, there are times where time is of the essence, and you must act immediately, but if the position is semi-locked, this strategy can be useful.
Aim for endgames that you are familiar with, and know how to win. This goes back to my very first point: Know basic theoretical endgames.