Sorry for asking, but where did you get that quote on Darkvision from? I don't remember reading that part on "unless it's invisible or has cover". This sentence rules out shadows, which i'm pretty sure it's not supposed to do.
1. Yes. It works exactly the same for a light-dependent creature in a well lit room with no cover around. It just means that normal darkness isn't a hindrance of any sort to a creature with darkvision within the ability's range.
2. As soon as a creature moves out of hiding and enters the range of your darkvision, it's detected. He might as well be walking, instead of hiding, outside the darkvision's range. However, it can catch you flatfooted if using a ranged weapon (ex.: you're holding a torch and the creature is farther than 60ft. away).
3. A creature would have to be hiding in a square from which it could attack you (either melee or ranged) and, if it's within the 60ft. range of your darkvision, you must fail the opposed "Spot" check. If the creature is outside the 60ft. range, you wouldn't be allowed a "Spot" check. Maybe a "Listen" check, to tell you something's lurking in the shadows ahead, but that wouldn't give any special advantage on this.
BTW, the
Hide skill description specifies that there must be some kind of cover close to the hiding creature to do so.
4. "Hide in Plain Sight" basically turns shadows within 10ft into cover. I'd rule it can hide from a creature with Darkvision.