Where do I find the serpent idol?
What do I do with the incense cones?
What key do I need to free H'Thark?
What use does the spider nectar have?

The serpent idol is to be found by opening the snake holding pens and swimming through an underground passageway.
The incense is used in a rite which will summon the spirit of the naga - if you do the ceremony correctly and answer the questions correctly, the really BIG snake head will open up allowing you access to the real naga.
I forget which key you need for the prisoner - will look that up and repost.
The spider nectar is also used in the summon naga spirit ceremony.

Wyv

the key to the prisoner is from the lizard head near the room with a hole bunch of boxes. He is the guy asking you if anyone knows that you are here in the snake temple,
he has the key.

Wyvern.... are the snake holding pins the place where the combination skull locks are? If so, I could not find a passageway anywhere. And Gaunty.... the location you gave me for the key is extremely vague. I honestly don't recall stumbling on a lizard head. Could you be more specific?

The Serpent Holds are downstairs, near the back entrance when you first enter the temple. You will need to use the Serpent key to open either door. In the easternmost chamber there's a switch on the wall. Flip it, then jump through the big hole in the back of the room and swim down the corridor. You'll find the Unholy Filth there, along with the Serpent Idol.

The Inquisitor is the one with the Monkey Key for H'Thark. You'll find him on the 2nd level of the main temple, on the southern side. If you go to the area that has all the Skull Lock combinations on it, return to the room that it branches from, go upstairs, and take the northern exit. The hallway curves back west and you'll see the Inquisitor just standing there in the hallway. Talk to him, pickpocket him, or kill him, but get the key.

Hope this helps,
Sazerac