I thought you said that any spells we cast before the scene automatically succeded? Or does that have something to do with studying resonance?
I was under the impression that you wanted to cast a new spell with a Mind 1 element, since you said you wanted to see "the things that the mind spell lets him search for."
Edit: Shouldn't it be Intelligence+Occult+1/2(Density modifier on pg 278) for 8/9 dice, not that those dice will help Joseph with his horrible luck or anything. As for the action, just keep going each 'round' until he gains some amount of successes, or unless he takes some other action.
No, because you don't know the rote. You're casting it improvised, so it's Gnosis + Prime. It should probably be Gnosis + Mind, actually, but I was being a little charitable in making Mind conjunctional, assuming you'd drop your current supernal vision for a new one with a Mind element. The Density modifier applies to attempts to scrutinize resonance; since I thought you were casting a new spell, I didn't factor it in.
I actually have no idea if I can use this to search for spirits or not. It seemed like a good idea, especially because of the lack of actual spirit interacting spells I have. But after reading, it seems like I have to be able to sense the object before I read its resonance. I don't even know anymore. If I can't find the spirits, its 8 dice on mages. If I can, I think its 9 dice. On the building itself, its only 5 dice.
Supernal Vision will only let you see things in the material world with your own, unaided senses, and scrutinize their resonance. You need a Spirit element to see into the Twilight, as Gabriel did.
Here's what I recommend now: Prometheus can cast Third Eye (Mind 1) with 5 dice to see Mind "stuff", or scrutinize with his existing Supernal Sight, and see everyone's Nature. That would gain you a +1 density bonus.
Incidentally, it would really help me if you noted the attributes and dice pool you're rolling when you do things, preferably in a format like:
[sblock=roll]Scrutinize other mages' resonance with Supernal Vision: Gnosis (3) + Prime (3) + Density Bonus (1) = 7 dice[/sblock]