You're skipping ahead, it seems.
If you've talked to Aurvandel and he hasn't helped you, and his icon is still on your map, then you haven't finished investigating Heime's disappearance. You've found an object where Heime was abducted. That object will help Aurvandel scry. Have you shown it to him? It won't show up in the dialogue options, you need to *show* him the object.
Hope this helps.
If you're really stuck:
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×Select Heime's sword in your inventory and click it on Aurvandel (he probably needs to be in his study, but I'm not sure). Once you do that, a cutscene will play, and the dialogue options concerning Svartalfheim will unlock.
Concerning your other questions:
Adventurer's guild:
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×How do you know about it? If you haven't been to Svartalfheim, you shouldn't yet be able to talk with the person who points you in the direction of the secret stash. ^^; But anyway, you mustn't put out the fire. You must protect yourself from it while you search for the button that opens up the hiding place. What fire-related spell do you know?
Icy flower:
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×It's an alchemy ingredient. It's used in potion making, but you'll need the recipe first!
Circle of flames:
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×That's indeed a later part of the game. Take care of Heime first, you'll be directed to the woman in the circle later on.
The swamp:
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×I'm not sure there's anything to do for the mage here, the plant creature is impervious to magic. This may be a fighter and/or a thief only quest.
[Last edited by PicaLudica at 12-30-2013 10:26 AM]