Awwww . . . the first egg broke!!

Well, Sweetpea & Daisy have been displaying mating behavior w/each other for a few weeks now & I've been expecting that they would start getting a little broody on me. When I opened the coop door yesterday morning, right next to the water dish was a distinctly orange circle which definitely looked like a yolk to me. Looking around, I didn't see any shell, so I was a bit concerned. Now, their water dish is about 4' from their bedding material on the opposite end of the coop. After they had left the coop for their breakfast, I went around to the back of the coop & opened it up & looked at the little nest that Sweetpea (I believe) had made, fully expecting to find an eggshell that she had maybe put back in the nest. No luck. While hosing down the coop, they seemed very concerned & came to the door of the run & watched me closely which they'd never done before. I added more hay & returned to the front of the coop to finish cleaning it out & hose down the ramp. When I picked up the water dish, there was an eggshell in it!! What gives?

What do you think happened? Why would she lay an egg outside the nest? The shell was very thin I noticed. Is this just nature's way of disposing of a "bad" egg?

Another question: Since I don't have a drake & won't be raising any ducklings but will be eating the eggs, do I just harvest the eggs each day? Will they continue to lay even though I take the eggs up? How do I clean the eggs w/o washing off the protective layer?

Sorry for all the questions but this is a first time experience for me, lol. I appreciate any advice anyone can give me.