user2971: After a trade that sacrified a bishop and a knight for two pawns and a rook, the game reached the following position: (White to move.)
[FEN "2r2qk1/1b1n1pb1/p4n1p/1p4p1/4P3/1BN2P2/PPP3PP/R2Q1RK1 w - - 0 17"]

At this point the engine was evaluating the position as -1.65.
I am confused with this evaluation. After this trade, white can go Qe2 and soon take claim of the open file with a rook and it seems that all white's pieces are with good activity and the pawn structure seems better than black's, so at first glance it seems to me that not only there is material advantage (white's up a pawn) but also a positional one.
I tried looking at the engine's suggested moves to see what I was missing and the moves are obscure to me. For instance, after 1.Qe2, the engine suggests 1...Bc6 and after 2.Rfd1 it suggests 2...Nh5. Both these moves don't seem to accomplish much to me. I can see a threat of jumping the knight to f4 eventually but it does not seem so dangerous. What makes some sense to me is that the bishop in g7 will probably be able to disrupt the pawns on the queenside either by doubling the pawns on the c-file by taking the knight or by taking on b2 if white has to move the knight due to b4 or some other threat. In any case, this should take some commitment and due to white's pieces' activity it seems that this might not be easy to go unpunished or simply stopped. Furthermore, this would justify to me perhaps an evaluation closer to 0, not -1.65.
Maybe worth noticing that the engine suggests 1.Qd2 instead of 1.Qe2, but analyzing this branch wasn't very fruitful either. For instance, one variation is as follows:
[FEN "2r2qk1/1b1n1pb1/p4n1p/1p4p1/4P3/1BN2P2/PPP3PP/R2Q1RK1 w - - 0 17"]

1.Qd2 a5 2.a3 a4 3.Ba2 Ne5 4.Rad1

At this point, the evaluation is at -0.83 and I don't see a clear problem either.
This is why I'd appreciate if someone can explain why the engine likes black in the first highlighted position so much.

user12554: To add to the other answers, Black's pieces are more active on the board than White's. They control more squares and  offer more options. White's rooks are a bit cramped. Although I'm not certain about it, I believe Stockfish takes this into account in its evaluation.

user10983: This might not answer your question as it already has some good ones. But just out of curiosity, I ran your game with two separate Stockfish engines, running at their full capacity. I wanted to see how the game would continue, assuming the players give their optimal moves. (The word optimal may not be the best choice in this context. Please take it with a grain of salt).
Here is the result:
[Title "StockFish vs. StockFish"]
[FEN "2r2qk1/1b1n1pb1/p4n1p/1p4p1/4P3/1BN2P2/PPP3PP/R2Q1RK1 w - - 0 17"]

1. Qd2 Nc5 2. Ne2 Nh5 3. g4 Rd8 4. Qa5 Nf6
5. Ng3 Rc8 6. Rad1 Ne8 7. c3 Nd6 8. Rfe1 Be5
9. Qb6 Kh7 10. Re2 Rc6 11. Qa5 Qe7 12. Bd5 Rc8
13. Kg2 Bxd5 14. Rxd5 Nc4 15. Qb4 Qa7 16. Nh5 Qb6
17. a4 Nxa4 18. Qe7 Qe6 19. Rd7 Kg6 20. Qxe6+ fxe6
21. Re7 Rc6 22. b3 Nxc3 23. Rf2 Ne3+ 24. Kh3 a5
25. Rd2 Ncd1 26. Rb7 Rd6 27. Rg7+ Bxg7 28. Rxd6 Nf2+
29. Kg3 Be5+ 30. Kxf2 Nxg4+ 31. fxg4 Bxd6 32. Ke3 Bxh2
33. Kd4 Bg1+ 34. Kd3 Kf7 35. e5 Ke7 36. Ke4 Kd7
37. Ng3 a4 38. Ne2 axb3 39. Kd3 Bh2 40. Kc3 Bxe5+
41. Kxb3 Kc6 42. Kb4 Bd6+ 43. Kb3 Kc5 44. Nc3 Be5
45. Ne4+ Kd5 46. Nd2 Bf4 47. Nf3 Ke4 48. Ne1 e5
49. Kc2 Bg3 50. Nd3 Kf3 51. Nc5 e4 52. Nb3 Kxg4
53. Nc5 e3 54. Kd3 Kf3 55. Nb3 Be5 56. Kc2 e2
57. Nd2+ Ke3 58. Kb3 Kxd2 59. Kb4 e1=Q 60. Kxb5 Qc1
61. Kb4 Qc6 62. Kb3 Qb5+ 63. Ka3 g4 64. Ka2 Qb2#

As you see, white is basically crippled after losing their bishop. Under different circumstances the result might have been different. But I think your engine's evaluation seem to be spot on.

user26557: 2 pieces for the rook is often better. In this position, black has a better position with more good squares for his pieces, and a clearer long term plan (attack kingside with good knights). The e5 square is a great square for the knight. The other knight can go Nh5-f4. The b2 pawn is weak and in the eye of the black bishop, which makes it harder for white to put his knight on d5. White's bishop is hitting a wall and no clear plan on how to improve it - black will just move his king and push pawns up. Black plans to break the kingside later on with a g4 push. The only plan for white is to double on d file and eventually put a knight on d5, which black is likely to be fine exchanging his bishop for.
In simple terms, a knight on e5 and another on f4 with a bishop x-raying b2 (limiting the white knight) and the rook x-raying c2 (limiting the white bishop) is a pretty clear advantage. Which side would you rather be?
Also, a knight on f4 is extremely dangerous for white - it would instantly become black's best piece. It's setting up for sacrifices, pawn pushes, and the queen swinging over to the kingside.

user12629: Interestingly, even without looking ahead and just evaluating the immediate position, Stockfish thinks Black is ahead by nearly half a pawn despite agreeing that White is ahead in raw material. Looking at the sub-scores, the "Imbalance" category is where most of Black's score is coming from.
"Imbalance" looks at which pieces are on the board and makes assumptions about how well they coordinate together. For example, each rook gets a bonus for each friendly knight and bishop but a penalty for other friendly pieces, and a penalty for enemy bishops and queens but a bonus for enemy knights and pawns.
In this position, Black is getting a bonus for having the bishop pair. White seems to be getting a penalty for having two rooks and a queen (the algorithm apparently thinks rooks don't work well with friendly rooks or queens) while Black's queen gets a bonus because the extra enemy rook and pawns are considered as potential targets just for existing. Overall the synergies between the various pieces actually give Black more of a score boost than the bishop pair itself does, and in total it's enough for Stockfish to think it outweighs the material deficit.

2971: <p>After a trade that sacrified a bishop and a knight for two pawns and a rook, the game reached the following position: (White to move.)</p>
<pre><code>[FEN &quot;2r2qk1/1b1n1pb1/p4n1p/1p4p1/4P3/1BN2P2/PPP3PP/R2Q1RK1 w - - 0 17&quot;]
</code></pre>
<p>At this point the engine was evaluating the position as -1.65.</p>
<p>I am confused with this evaluation. After this trade, white can go Qe2 and soon take claim of the open file with a rook and it seems that all white's pieces are with good activity and the pawn structure seems better than black's, so at first glance it seems to me that not only there is material advantage (white's up a pawn) but also a positional one.</p>
<p>I tried looking at the engine's suggested moves to see what I was missing and the moves are obscure to me. For instance, after 1.Qe2, the engine suggests 1...Bc6 and after 2.Rfd1 it suggests 2...Nh5. Both these moves don't seem to accomplish much to me. I can see a threat of jumping the knight to f4 eventually but it does not seem so dangerous. What makes some sense to me is that the bishop in g7 will probably be able to disrupt the pawns on the queenside either by doubling the pawns on the c-file by taking the knight or by taking on b2 if white has to move the knight due to b4 or some other threat. In any case, this should take some commitment and due to white's pieces' activity it seems that this might not be easy to go unpunished or simply stopped. Furthermore, this would justify to me perhaps an evaluation closer to 0, not -1.65.</p>
<p>Maybe worth noticing that the engine suggests 1.Qd2 instead of 1.Qe2, but analyzing this branch wasn't very fruitful either. For instance, one variation is as follows:</p>
<pre><code>[FEN &quot;2r2qk1/1b1n1pb1/p4n1p/1p4p1/4P3/1BN2P2/PPP3PP/R2Q1RK1 w - - 0 17&quot;]

1.Qd2 a5 2.a3 a4 3.Ba2 Ne5 4.Rad1
</code></pre>
<p>At this point, the evaluation is at -0.83 and I don't see a clear problem either.</p>
<p>This is why I'd appreciate if someone can explain why the engine likes black in the first highlighted position so much.</p>
 12554: <p>To add to the other answers, Black's pieces are more active on the board than White's. They control more squares and  offer more options. White's rooks are a bit cramped. Although I'm not certain about it, I believe Stockfish takes this into account in its evaluation.</p>
 10983: <p>This might not answer your question as it already has some good ones. But just out of curiosity, I ran your game with two separate Stockfish engines, running at their full capacity. I wanted to see how the game would continue, assuming the players give their optimal moves. (The word <em>optimal</em> may not be the best choice in this context. Please take it with a grain of salt).</p>
<p>Here is the result:</p>
<pre><code>[Title &quot;StockFish vs. StockFish&quot;]
[FEN &quot;2r2qk1/1b1n1pb1/p4n1p/1p4p1/4P3/1BN2P2/PPP3PP/R2Q1RK1 w - - 0 17&quot;]

1. Qd2 Nc5 2. Ne2 Nh5 3. g4 Rd8 4. Qa5 Nf6
5. Ng3 Rc8 6. Rad1 Ne8 7. c3 Nd6 8. Rfe1 Be5
9. Qb6 Kh7 10. Re2 Rc6 11. Qa5 Qe7 12. Bd5 Rc8
13. Kg2 Bxd5 14. Rxd5 Nc4 15. Qb4 Qa7 16. Nh5 Qb6
17. a4 Nxa4 18. Qe7 Qe6 19. Rd7 Kg6 20. Qxe6+ fxe6
21. Re7 Rc6 22. b3 Nxc3 23. Rf2 Ne3+ 24. Kh3 a5
25. Rd2 Ncd1 26. Rb7 Rd6 27. Rg7+ Bxg7 28. Rxd6 Nf2+
29. Kg3 Be5+ 30. Kxf2 Nxg4+ 31. fxg4 Bxd6 32. Ke3 Bxh2
33. Kd4 Bg1+ 34. Kd3 Kf7 35. e5 Ke7 36. Ke4 Kd7
37. Ng3 a4 38. Ne2 axb3 39. Kd3 Bh2 40. Kc3 Bxe5+
41. Kxb3 Kc6 42. Kb4 Bd6+ 43. Kb3 Kc5 44. Nc3 Be5
45. Ne4+ Kd5 46. Nd2 Bf4 47. Nf3 Ke4 48. Ne1 e5
49. Kc2 Bg3 50. Nd3 Kf3 51. Nc5 e4 52. Nb3 Kxg4
53. Nc5 e3 54. Kd3 Kf3 55. Nb3 Be5 56. Kc2 e2
57. Nd2+ Ke3 58. Kb3 Kxd2 59. Kb4 e1=Q 60. Kxb5 Qc1
61. Kb4 Qc6 62. Kb3 Qb5+ 63. Ka3 g4 64. Ka2 Qb2#
</code></pre>
<p>As you see, white is basically crippled after losing their bishop. Under different circumstances the result might have been different. But I think your engine's evaluation seem to be spot on.</p>
 26557: <p>2 pieces for the rook is often better. In this position, black has a better position with more good squares for his pieces, and a clearer long term plan (attack kingside with good knights). The e5 square is a great square for the knight. The other knight can go Nh5-f4. The b2 pawn is weak and in the eye of the black bishop, which makes it harder for white to put his knight on d5. White's bishop is hitting a wall and no clear plan on how to improve it - black will just move his king and push pawns up. Black plans to break the kingside later on with a g4 push. The only plan for white is to double on d file and eventually put a knight on d5, which black is likely to be fine exchanging his bishop for.</p>
<p>In simple terms, a knight on e5 and another on f4 with a bishop x-raying b2 (limiting the white knight) and the rook x-raying c2 (limiting the white bishop) is a pretty clear advantage. Which side would you rather be?</p>
<p>Also, a knight on f4 is extremely dangerous for white - it would instantly become black's best piece. It's setting up for sacrifices, pawn pushes, and the queen swinging over to the kingside.</p>
 12629: <p>Interestingly, even without looking ahead and just evaluating the immediate position, Stockfish thinks Black is ahead by nearly half a pawn despite agreeing that White is ahead in raw material. Looking at the sub-scores, the &quot;Imbalance&quot; category is where most of Black's score is coming from.</p>
<p>&quot;Imbalance&quot; looks at which pieces are on the board and makes assumptions about how well they coordinate together. For example, each rook gets a bonus for each friendly knight and bishop but a penalty for other friendly pieces, and a penalty for enemy bishops and queens but a bonus for enemy knights and pawns.</p>
<p>In this position, Black is getting a bonus for having the bishop pair. White seems to be getting a penalty for having two rooks and a queen (the algorithm apparently thinks rooks don't work well with friendly rooks or queens) while Black's queen gets a bonus because the extra enemy rook and pawns are considered as potential targets just for existing. Overall the synergies between the various pieces actually give Black more of a score boost than the bishop pair itself does, and in total it's enough for Stockfish to think it outweighs the material deficit.</p>
