Engine says at the very moment i exchanged my rook for a knight, game turned into a dead draw. Really? Was that decision that bad.. I though i had a good winning chance with one step ahead on the remaining pawns. And thought i pushed the wrong pawn in the process.. But this shows my destiny was set very before.
I'm having hard time to believe this.
You literally had a free pawn on a7 after Nf4. That's your strategy. Take advantage of your rook's range. Sacking it for the knight made zero sense. What did you think was gonna happen, why would that be a winning pawn endgame? Equal number of pawns, your king is not more active (black king is, in fact). His two pawns being isolated is not nearly enough. Even if there was no pawn on c6, it'd still not that hard to screw up and draw, with the pawn on c6 there's just nothing.
I honestly don't know, it made perfect sense at the moment i played it 
then i realized it was a mistake..
Well, black's a-pawn is helpless against Rg7, it can delay the capture by moving forward then Ra7 and it would be a winning endgame for white.
So the answer of my question; rooks are priceless in pawn endgames, do not trade them and collect as many pawns as you can.
It's just that these types of endgames are a perfect illustration of rook's superiority against a minor piece. Knight especially, since it can't make waiting moves.
Here, you might even sac you rook for the knight (given you're in time trouble and don't want to constantly worry about being forked), but only after you have more pawns than black does. You might wanna build some experience in pawn endgames so that you have a better idea when it's good to trade down.
I was in time trouble and exchanged a rook for a knight and tried to push enemy king a bit far away from the remained pawns but unfortunately he got opposition and i had to go for a threefold repetititon draw.
What i did here was obviously not the correct way to play this type of endgames. I wonder how i should have played here. Should i have kept knight in pin and approached my king to the pawns?
Engine probably will suggest me a winning tactic here (which i could have found myself if i hadnt been in time trouble) but I need a general approach. What should be my goal here?