I guess this is probably the best explaination.
Also, spoilers!
Sorry, it's the Lore forum. Spoilers are implied. You should be really careful reading this place if you don't want spoilers, cause most of the time spoiler tags are just not used.
Yes, but I don't think we got the whole story on why they acted during that quest. Only 3 guys show up, and no one who introduced themselves as being the head of the Order or really anyone with authority. My impression (and this is just my own opinion) is that there are likely factions within the Order, and it's possible that the onaes who showed up were doing something against what most of the others would have wanted.
This was mentioned on a previous thread, but one suggestion is that the quest wasn't just to take the Eye of Magnus away, but to assassinate a member of the Thalmor.
I seriously doubt it, that Thalmor guy wasn't important enough to warrant assassination, after all he was an emmisary to a backwater mages guild like thing, with no real power at all... That probably means the Thalmor wasn't that great either. Wereas the eye of Magnus demonstrated clear power... As for the different factions, it could be. I have absolutely no idea on how the order works. They seem to me like a more open order with a headmaster to judge in case things go wrong or conflicts arise. But that's just an assumption.