Interesting end game. Your right about his Queenside pawns, I think he should have had a passed pawn and won.
beginner game
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8.Nxe5 punishes 7...Nd4 ? (White wins a pawn).
10.fxe3 !? was worth consideration (opening the f file, keeping control of d4).
12.h3 is useless (if ...Ng4 Qg3, and then ?). 12.f4 maybe (I don't have any clear-cut plan here).
13.a3 ? (useless) : ...c5 (?) weakened the d5 square ; that's why Bd5 or Nd5 is better (rather the bishop).
move 20 : f5 is not a passed pawn. A passed pawn is a pawn that has no enemy pawns preventing him to run to promotion. Here if f5 advances, he get caught by ...g7xf6 at some times. (that was just a terminology remark - the move were good).
21.Qxe5 wins another pawn and most probably ends up any Black resistance.
22.Qg3 ? has no sense. But 22...e4 ? neither : 23.Qe3 (lol) wins the pawn after ...Re8 Re1 (black cannot take d3 because of the pin, and f5 will be defended after dxe4).
26.Qb3+ ?? probably is a lost pawn endgame (Black's future passed pawn is very far, and after White will take it and Black will take the e pawn, Black's king is closer to the remaining pawns).
Here you need to know that in queen endgames, the material (number of pawns) in not very important, and the two main features are king safety and advanced passed pawns. Knowing that, I'm pretty sure this is won for White due to the e passed pawn. I bet either 26.e5 or 26.Qb8+ followed soon by e5 wins.
Skip the following part if you are not interested in the analysis of the pawn endgame.
Black misplayed the endgame. In such pawn endgames, with some passers-to-be on both wings and no other special feature, my reasoning goes :
(I do not post diagrams on intent, start with the position after White's 27th move in sight and try to play the moves in your head - it's good training).
1- can I even at the cost of many pawns, make the way free for one of my pawns to promote, without the enemy king being able to catch it ? Here the answer is no : the line I calculate in my mind is 27...c4 28.bxc4 bxc4 29.Kf2 and the king catches the pawn.
Another try is (27...a5 28.Kf2 as in the game) 28...c4 29.bxc4 b4 30.axb4 a4 and the king cannot catch the pawn, but 31.b5 (or c5 with the same idea) a3 32.b6 a2 33.b7 a1=Q (not on check !) 34.b8=Q+ and the queen endgame is much probably lost. So I go to :
2- By activating the king, what does he need to do ? Here he is obviously needed to take care of the passed e pawn. Thus the way to go is Kg8-f7-e6-e5, and after that, if White defends the pawn, create a passed pawn on the Qside, as far as possible of his king. Here however, I am forced to create it on the c file (or I will lose a pawn, and now his king is close enough to stop my passer). However, I wait for this and I push g and h as far as possible first (see next steps for the 'why'). I keep the a pawn behind to force him lose time picking it if he tries to promote his a pawn after taking on c. As soon as he goes after my pawn on the c file, I take his on the e file, then I rush eating the g and h pawn. As I correctly advanced g and h before creating the c passed pawn which lets him attack on the Qside, I won some tempi in the promotion rush. -+
Well guys I have followed the advice of many and played a 30 minute game and have done my best to analyze it. I enjoyed this game alot. Please tell me what you think.