The idea of hitting something you can't detect inside a room is explicitly allowed, as described on pg. 81 of Hermetic Projects - in the discussion of "how do I get rid of an Intangible Tunnel?" the answer is "first perceive it, then cast Unravelling the form of Vim on it - or cast it on the entire room, if you can't directly perceive it." You don't even need to know for sure that it's there - the text explicitly allows for sufficiently paranoid magi to cast it.
Also, I"m pretty sure that if you have an Arcane Connection to 1 person, and cast a Group spell through a tunnel, it will affect everyone in any gropu that the AC'd target is in. For the same reason that if you see someone's head or hand, you can affect their entire body. Thus, those invisible targets may very well be hit with any relevant spell.
Also, you can hit invisible targets accidentally, or if you have a vague notion of where they MIGHT be, according to the "How to hit invisible targets" section in HoH:S. As such, you can probably hit invisible targets that are inside a group as well.
This tells me that magical attacks are auto-hit, and they have a more-or-less defined area around them that they also auto-hit. So, you can aim for a point of ground, and automatically hit it - and if there are a combination of visible and invisible targets in that area, then you'll hit all of them. Its just that Ars Magica combat is vauge enough that "where is everybody standing" is a bit of an abstract question.
Of course, if a mage can restrict their magical sizing to "the 6 peasents I see", then sure - but I'm not aware if magi can do that freely. (Finesse roll? I'd allow it.) But I think if the invisible peasents around the corner are close enough to be a part of the group, then they're affected - assuming the group doesn't get too large as a result.
They can. It burns off their Might pool first, at which point they loose the possession - and then it starts in on their permanent Might.
EDIT - huh. Actually, it's a bit unclear. RoP:I pg. 33 says "Vim spells may be used on the energumen to target the demon rather than the host; these must overcome the demon's Infernal Might in the usual way, but drain the Possession Might pool, not the Infernal Might."
Which is my understanding. However, Rop:I pg. 121 has a new guideline "Reduces a target's Might Pool"; there's also a spell (pg. 122) that uses this that affects a demon that is possessing someone, but only affects their Might pool.
So, the first seems to suggest that you can just DEO a possessed individual, and it will affect their Might Pool, and then their Might. But the latter suggests you may need to create a separate spell for it.
I would interpret that to mean that you can DEO a demon that is possessing someone just fine (and it burns off their Might pool, and then their might.) However, if the demon is only partially possessing them (they can do that - they invest Might points into the target, but don't physically enter them), then you'd have to use the "burn off might points" spell to clean them out.