Did Deep Blue play like a human? Kasparov said, in Game Over: Kasparov and the Machine, that Deep Blue "sank into deep thinking" and took like 15 minutes to make a move.

The movie tells the story of their match, in 1997.

At a certain position, in the second game, Deep Blue could have taken two pawns, but did not, aiming for a win in the long run.

Do modern computers agree with Deep Blue on that, and, if they do, how long does it take them to find the correct winning move?

That part of the movie can be watched here.
This article from Chessbase answers most of your questions.

This was the position in which Kasparov had set a "computer chess" trap.

 [fen "r1r1q1k1/6p1/p2b1p1p/1p1PpP2/PPp5/2P4P/R1B2QP1/R5K1 w - - 0 35"]
[White "Deep Blue"]
[Black "Gary Kasparov"]


He was expecting 
36. Qb6 Rd8
37. ab Rab8
38. Qxa6 e4

 [fen "1r1rq1k1/6p1/Q2b1p1p/1P1P1P2/1Pp1p3/2P4P/R1B3P1/R5K1 w - - 0 35"]
[White "Deep Blue"]
[Black "Gary Kasparov"]


when, for the cost of 2 pawns he has generated dangerous counterplay based on the idea of Qe5 possibly followed by e3.

Instead Deep Blue played the immediate ab followed by Be4 thereby nipping in the bud any chances of counterplay via ... e4 and ... Qe5 for black.

According to the article -


  In fact, if you consult any of the top engines of today, whether it be
  Houdini 4, Stockfish 6, or Komodo 8, they all choose Deep Blue's move
  36.axb5. For example:
  
  Komodo 8: 36.axb5 axb5 37.Be4 Qd8 38.Kh2 Rcb8 39.Ra6 Kf8 40.R6a5 Kg8
  41.R1a2 Rxa5 42.Rxa5 Bc7 43.Ra1 Bb6
  
  +/- (0.84) Depth: 29 00:02:15 686MN, tb=57


So, nothing to see here (2 min 15 sec for the computer) ;-) Move on!