Does Pilfering Swarm Stack with Desecrate?

Sadly no because you cant 'remove' or have two abilities holding an enemy. If dome steals from swarm (vise versa) then the previous effect is gone since the requisite for either is for the enemy to be in the captured state of the ability.

Does pilfering swarm have to kill?

The Pilfering Swarm Augment Mod will now generate drops for enemies that are slain being held by tentacles, not just dying from the tentacle's appearing. In short, enemies don't need to be killed by the tentacles to have an added drop chance.

Does Hydroid and Nekros stack 2020?

So yes you can stack nekros now for a higher chance to get loot from each cropse/bodypart. So with a frost and 3 nekros you have 100% dismemberment and 3 chances to roll extra loot from each part.