[RPG] What Pets or Livestock Would Drow Have

Looking on the poisons table in the Dungeon Master's Guide, page 297, the poisons table lists the Primary effect of Drow Poison as Unconsciousness and the Secondary effect as Unconsciousness for 2d4 hours, with no mention of the ambiguous "remain unconscious" language. So it appears that the answer to your question is Yes, the character must roll both saving throws.

There is no "generic" answer, like everything else about D&D it varies by game world.

In Paizo's Golarion campaign setting, then your key references are the Second Darkness Adventure Path and the Into the Darklands campaign setting book. Generally they keep as slaves "whoever they can get their hands on that is useful and tractable." This includes everything from troglodytes to other drow to surface folk to driders to dark creepers to "balor-possessed greater water elementals" (all these are listed as slaves in that drow city you're talking about).

To drow mores, anything and anyone who is not a drow is a candidate for slavery. Their word for servitor is anquestra, while their word for outlander is jenanquestrok, which means “not yet a slave.” Sentients that are spoils of war are always considered slaves, especially if the purpose of the war is to gather more servitors. Similarly, non-drow trespassers can be declared anquestra, and this can happen even to non-drow offered protection from a noble house, should another noble house want to enslave them.

In the drow culture part of The Armageddon Echo it says "drow don't enslave other drow, but some do become servants" and then in Endless Night it refers to drow slaves about a zillion times, who seem to meet the standard end of slaves, so YMMV.

If you want a list of other darklands races that might be good candidates, consider checking out the Pathfinder Wiki's Darklands and subsidiary entries, or the list of creatures whose habitat is underground from the d20PFSRD.