Right now we're not displaying descriptions on the battle pet ability API, but want to add it soon.

Once I do these are the ability id's of the type passives:
http://us.battle.net/api/wow/battlePet/ability/238
http://us.battle.net/api/wow/battlePet/ability/245
http://us.battle.net/api/wow/battlePet/ability/239
http://us.battle.net/api/wow/battlePet/ability/242
http://us.battle.net/api/wow/battlePet/ability/236
http://us.battle.net/api/wow/battlePet/ability/243
http://us.battle.net/api/wow/battlePet/ability/241
http://us.battle.net/api/wow/battlePet/ability/237
http://us.battle.net/api/wow/battlePet/ability/240
http://us.battle.net/api/wow/battlePet/ability/244

Most battle pet ability tooltips show hints about what types they are good or bad against as part of the tooltip. This boolean controls that. Right now it's actually named opposite of what it should be. In a future update it will change to "hideHints"

On a normal pet ability this is set to false and in tooltips we render the strong/weak hints along with the description.
http://us.battle.net/api/wow/battlePet/ability/231

On the passive type abilities (for example) the inverse hints are already included in the description (Right now since descriptions aren't show I know this doesn't mean much) so this flag is set to true so that we don't also add in the normal type helpers.
http://us.battle.net/api/wow/battlePet/ability/238

Thanks a ton! If I may ask one more question, what are the slot and order fields used for?

If I may be a bit more specific: I'm trying to figure out which abilities someone has selected on their pet. I thought that the slot value would correspond to the actual slot in the ui (0-indexed, so going 0,1,2 would be the first 2nd 3rd slots) and that the order corresponded to the order in which they're unlocked, as the order (being 0-indexed) seemed to correspond to the levels they're unlocked, only that the last 3 abilities slot numbers were almost as identical as the first 3 abilities.

When viewing an ability without the context of a species, there is no slot/order.

When viewing an ability within the context of a species the slot is which vertical row the ability is in. The abilities with the same slot id represent the choice the user can make about which ability to have available.

The order is for UI display and represents (as you assumed):
0 1 2
3 4 5

We only have selected ability data for the pets in your battle pet slots. In the petSlots section of the character profile api we list the three abilities that a user has selected for that pet slot.