As Black, when given a choice of taking the White's pawn, for what reason should I consider taking d5 pawn with e6 pawn? Wouldn't this open up the king's file and put it at risk of being attacked in the future?
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The main point of the engine recommending exd5 is because it opens up the diagonal from c8 to h3. By playing an early e6, the bad light squared bishop is really weak and has terrible scope, which is why taking with the e pawn could be followed with developing your bishop onto a square on a more open, free diagonal in the future. As long as you castle and don't open up any kingside files, you should be good. As long as your king is safe, an open e file won't do much damage, as his e-pawn is stuck on e-3 (notice white's dark squared bishop; it's basically stuck).
fyi: The whole point of the Slav Defense is to decline the Queen's Gambit with a pawn without playing e6 to block your light squared bishop.
The "e" columns being open is not an issue for king safety. Your king is only there temporarely. After ...exd5, Black would probably follow with ...Bd6 and ...0-0, then at some point ...Re8 to exploit the semi-open file.
...cxd5 is a playable alternative, but your c8 bishop would become a much worse piece. It's hard to see how you'll liberate him with an ...e5 breakthrough, so he'll stay "trapped" behind your pawn chain for a long time. White could also have the opportunity to play quickly on the queenside with Bd2 and Rc1.
Finally, after ...Nxd5 we are probably leaving too much space for our oppoennt on the center (we're allowing an e4 push)
