To reap the first eggs, or not to reap?

I found today my chickens’ first eggs in the coop.
I would very much appreciate any suggestion you could give on :

1) Whether or not I should take them immediately, or perhaps leave them in for a bit and wait ‘til a moment the hens are far away to not “traumatise” them :-)

2) Whether I should place an egg somewhere where I want them to lay in the future, away from danger of course.

3) (I’d made them two nests, but I assume it was the ducks in the coop to destroy them…) Whether or not and how I should make them another nest.

4) General behaviour I should have with and for them.

Thanks!