Demons are not stated to have any special sense of the Divine, nut ifit works for the story, sure. However, priests are easy to spot - they have tonsures.
I don't see why demons would have that ability. However, a demon might have Sense Holiness & Unholiness itself, and thereny be able to tell.
Probably not. The demon will know, however, and it is controlling their actions.
Your call. Maybe they're in a living hell where they watch but cannot control, maybe they lose time and have no idea, maybe they just remember it as a dream, maybe it's back and forth - sure. It pronanly won't be the same for two different possessions by different demons. Whatever works best for your story, your Saga, your players.
2 demons in possession of 2 individuals might recognize each other by smell or act or "feeling" - or not. But working together just seems the way of the Forces of Darkness.
The whole thing would be based on the demons' abilites. As I read the rulebook there are stupid and intelligent demons, too.
I think for greater demons sensing holiness an unholiness sounds cool.
Knowing the actions while under possession should be based on the goals of the demon. Does it help to seduce the target?
Generally I wouldn't limit the pc's supernatural skills because they cost a lot to be effective.
Actually reading the Divine book, it implies that demons can sense and feel the presence of holiness and it draws or repels them. The strong case for this is under the effects of being holy magus and how it draws demons to you to torment and tempt you.