Does White actually have any advantage?
No, White has no advantage here whatsoever. With proper play, the game should end in a draw.
Why I am I so certain that White has nothing in this position? Well, let us analyze the position using the diagram I submitted below:
Red color represent squares that Black knight control, while pink color represents squares controlled by Black pawns. Green color represents squares on which Black king can penetrate into White camp.
By looking at the diagram, you can clearly see the barrier knight and pawns on the queenside create for the White king. You can see that Black has sealed the queenside and White can not create any counterplay there.
White can not penetrate through center of the board either, as we can clearly see on the diagram, since
e6 pawns and knight block entry points.
This leaves kingside as the last hope, but Black king has a route ( marked with green color ) that can take to prevent White king to penetrate. White can not stop Black king to take this route.
Black bishop has no targets to attack, and is bound to the defense of the
d4 pawn. This pawn is a serious weakness in White camp and the biggest problem is that White can not get rid of it.
Black knight is very well posted, and restricts White pieces to the defense of the weak pawn. Black king is about to get active as well.
White must play
g4! in order to prevent Black king from penetrating. After that move he has sufficient resources to defend with ease.
What should White's plan be to try and win
White must wait for a mistake, after playing
are there any particular pawn structures White should aim for?
White has better minor piece for the endgame, but that weak pawn hinders him to utilize his advantage. In endgames, bishop is always stronger than a knight, if the side with the bishop has no weaknesses.
White should strive to create imbalance by forcing Black somehow to play
...e5. The passed pawn is nothing special as it is central one, and bishop is fast enough to catch it on time, so Black would not have much.
On the other hand, after
...e5, white should aim to create a passed
h pawn in order to play for the win. That pawn should reach
h6 so the bishop could defend it from afar, while keeping "an eye" on the Black passed pawn.
This would tie Black king/knight to the proximity of the White passed pawn, enabling White king to possibly penetrate on the queenside.
Of course, this is all hypothetical talking, Black would never allow such a thing to happen. Your question was about winning pawn structure, so my answer is to get the pawn structure where you have passed
h pawn, and
d pawn is exchanged. That is the pawn structure White should aim for.
Your second diagram looks very promising, but at the moment I have no time to analyze it. I believe you could have won with slightly better play. He (or she?) made such terrible moves, that if pressured just for few more moves, he/she would crack ( I am 100% sure of this ). Maybe I will update this post with thorough analysis ->let us hope that I will solve the problems at work.
Best regards, feel free to leave a comment if you need help or you have anny follow up questions.