I think Chevy survives and is able to hire another coach. My guess is that he has until the end of Hellebuyck's contract to fix things or someone else will get a chance to fix things.

First then an NHL GM or ACGM should look when trading is other teams cap. Sending away cap, especially multi year cap, without receiving similar cap rarely happens now.
The NHL seems to rehire the same guys. Look for Benning and Chiarelli as candidates.....I'm kinda joking, but good chance it's a familar name.

Value wise I think the Ranger trade is pretty good, but the Jets should be asking for Schneider as he plays more of a style that the Jets need than Lundqvist does. I also don't think Chytil adds much value to the deal.

Rangers decline. We need to keep some of our young cost controlled players (especially forwards).

What about swap Laf or Schnider and a 2nd

The picks are fine. I don't believe the Rangers would trade Schneider. Jones and Robertson would probably be their preferred defensive trade pieces along with Kravtsov.