What are the specifics on the Clairvoyance spell? I know it shows a path, but like what does dual-casting it do? How do you use it to raise your Illusion skill?
I don't think it serves any purpose at all other than giving you a direction towards your next marker, as far as leveling, I would assume you would get a few minor points for using the spell, but not necessarily for the spell affecting anything and giving you a damage bonus
It displays a path to an objective. It is illusion school, and I have never unlocked illusion dual-casting. It is very inefficient at raising illusion, if at all it does so. I have never noticed it raise a skill level for illusion - but I have never explicitly checked. It is a more immersive way of playing, with quest markers toggled off, but is naturally less powerful.
It can only display a path when...it can calculate a path, and will not be able to do so when far from basic ground terrain - boulders are not ground terrain. In this case it will fizz and pffft and a message will display that no path was found.
There is an order of priority for the path:
1) A player defined map marker overrides all others. So, be careful to ensure you are following the quest marker and not one you accidentally placed when checking the map
2) When multiple quests are active, I believe it chooses the most recently updated quest.
3) When a quest has multiple different types (e.g. two different NPC) targets only one path (unfortunately) will display. I believe this gives precedence to a lower queststage id of the target. Be careful as, unlike with quest markers on the map, you may not realise that there are alternative ways of completing a quest - even when reading the details of the quest in the journal. Todd's "Morrowind level of quest text detail" claim was nonsense.
4) When a quest has multiple specific objects, e.g. 3 unique books, then it will target the closest. It will not show a path to a non-unique item required (e.g. 10 fire salts) - the item instance must be explicitly defined for the quest (somewhere in the quest files).
I know nothing else about it, and my observations are probably imperfect =)
EDIT: I forgot to add a point about water. It will try and circumvent water, even if a short swim is quicker, but if it cannot find a path around then it will lead you to the water - but not through the water.
Duel casting just increases the range of the path shown to your objective. Its probably about twice as long. Doesn't really make all that much difference however, 1 handed does the job fine.