My last 2e Carnifex sighting involved dropping a Melta round from an Imperial Guard Griffon mortar directly on top of it; one shot, one kill.
10e has separated the missions completely from the rulebook;
GW releases them annually as card packs (and then they tend to screw up the allocations, making them hard to find).
This the current pack. It's made up of i) deployment zones; ii) primary missions (you'll have one per game); iii) secondary missions (each player will draw their own, and often you'll be drawing them every turn, as you complete and/or discard the ones you currently have); iv) "Challenger" cards (if one player falls behind on points, can give them a little boost towards catching up); and v) Twist cards, which nobody uses because they're wild swings. It also has a little rules pamphlet explaining how to use all these things in the context of a game.
All the primary missions they've released in 10e also start scoring in round 2, but usually in the Command phase (before any Reserves could arrive on turn 2).