The city it happens in isn’t New York-scale but an empty building (aside from Nate and Chloe) is shot down and crumbles during the helicopter battle in Desperate Times.
A villain blows himself up with a grenade, although he's mainly trying to kill the good guys. Nate can also jump to his death with appropriate reactions from other characters (he respawns).
There are blood splatters when you shoot enemies, the worst instance of this is the yeti that you have to shoot in the head repeatedly since the bleeding effect is repeated dozens of times.