I am curious whether the abilities granted from the Slasher feat from Tasha's Cauldron of Everything (p. 81) would work on swarms. More specifically, the second and third benefits:
Once per turn when you hit a creature with an attack that deals slashing damage, you can reduce the speed of the target by 10 feet until the start of your next turn.
When you score a critical hit that deals slashing damage to a creature, you grievously wound it. Until the start of your next turn, the target has disadvantage on all attack rolls.
The argument is that using the Slasher feat to lower an opponent's speed would likely consist of something along the lines of slashing at the legs or heel, or something along those lines, to debilitate your foes. Or on that crit you could be slashing a big gap out of an attacking creature's arm or hand…
If the creatures in a swarm are constantly dying as the swarm's HP drops (assuming this is how it works based on the damage drop when swarms hit half HP), then would these abilities technically work on a swarm or not?
Yes, the Slasher feat still works on swarms
Simply put, a swarm is still treated as a single creature for the purposes of stat-blocks and rules. There are no other special rules anywhere for swarms other than the abilities that are actually indicated in a swarm's stat-blocks.
These abilities do tend to have common features to represent the "swarm-i-ness" of the creature. E.g. Resistance to piercing and slashing and the "Swarm" ability to occupy another creature's space.
But beyond that there are no special rules. A swarm with resistance to slashing damage would take half damage from your slashing attack but would still be subject to the additional effects of your Slasher feat.
A DM could overrule this of course if they think it just doesn't make sense. Although in my opinion it's a matter of interpretation. For example, perhaps your slashing attack agitates the coherence of the swarm enough that it can't move or attack as effectively until it regroups!