That would be PvE only. Destiny Tracker tells you if you have kills with an exotic weapon (PvE) that you don't own, it counts those near you. Your PvP stats are your own.
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This is definitely incorrect information. I have gotten grimoire progress towards kills in PvP using certain classes in different classes than the one I was using. It was usually when I would play with a fireteam that I would notice this happening. Long story short, it does indeed happen in PvP.
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Well, I don't know where the 30% came from. What I'm seeing is 70% precision kill. http://destinytracker.com/destiny/medals/xbox/jester%20of%20sins [spoiler]Maybe its a typo[/spoiler]