Quest question.

I just started playing a few days ago and this is my first Elder Scrolls game so I'm still figuring a lot out but I have a question about quests.

While wandering the countryside I stumbled across "Dead Man's Respite", some Googling tells me that this is related to the "Tending the Flame" quest of the Bard's College.

If I finish this quest now without having been given the quest will I still get credit for completing it later?

In general can I stumble into dungeons without worrying about spoiling quests down the road?

Thanks.