Umm, so for some reason it says my dungeon instance is over a day old and it wants me to reset. Should I? Can someone explain what would happen if I chose either choice?

You don't have to reset it, but you can. Resetting the dungeon will start you back at the very beginning.

Is there some special reward for completing it I under a day?

No but you can only complete it once a day. So if you were halfway through but wanted to go through all the bosses instead of just what you have left, you can restart it.

Ok I think I will do that.

How do I reset? I didn't write down the number at the beginning :\

If you wait for at least 24 hours after you started the dungeon, there should be a notice saying your dungeon is over a day old, and an option asking if you want to reset it.

SPOILER ALERT! Re: the ending
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I chose "Sparkling" and received a Purple Relic. Chose the same thing a second time--another Purple Relic. Third time--over 4k gold. Fourth time (I did complete the slider puzzle this time)--3983 gold. Hypothesis: there is a pattern, but individual users potentially have different patterns.