I cant figure out how to purify the pagan temple in act 2. i found a walkthrough that says i have to talk with the statue again after i defeat the 3 guardian spirits.
But there is no talk option and i tried an earlier save where i killed the spirits again. Do i need a specific item to purify the temple?

I did this a week ago...i don't remember a problem. One thing though i was carrying some vials of holy water and at some point in act 2 i noticed one of them had gone from my inventory- so maybe it was used up at the Temple and i didn't notice? The Priest that gives you the quest also gave you a holy water dispenser (that doesn't show in the inventory) but maybe you also need a vial of holy water as well? I'm not sure if that's the solution, but it may be worth a try. The Priests that sell potions usually sell Holy Water.

due to other quests i always carry holy water with me. I dont remember him giving me a holy water dispenser, but if it doesnt show up in inventory i can not check it :(

is this quest important for the main quest/evidence gathering?

My memory of this quest has come back a bit and i now remember i had the same issue at first. For me it wasn't a bug, i simply hadn't cleared all the undead from the entire map, i think the Priest may have even mentioned clearing away the area. Once i did that it worked for me. If you have already cleared the map then I am out of ideas, sorry.
I don't believe the quest is essential to finish the game as it doesn't really relate to the main investigation, but it will prevent at least one other follow up quest (Foundation Stone).

After you defeat all three ghosts you should be able to "talk" to the temple again to consecrate it. But to do that you need Aspergillum (given to you by Judge Welfhar when receiving the quest from him). I think it should be visible in your inventory as any other quest item is. If you do not have it, it is possible you dropped it or destroyed it. In that case, you could add it with a console command:
- press ~ (next to 1)
- type \givenewitem Kropitko
- press Enter. Tinthan should be waiting for you near a fountain in Northwest Alvaron.

EDIT: No, that's a mistake. Please see my post in your thread "Where is thintan?" for more information.