Answer: Eggs of Fasciola hepatica or Fasciolopsis buski.
As pointed out by Florida Fan, this diagnosis can be made based on the large size of the egg (> 100 micrometers in diameter) and presence of an operculum. Several other readers also pointed out that the size is an important feature in differentiating F. hepatica/F. buski eggs from the similar-appearing but smaller eggs of Diphyllobothrium and Paragonimus. Unfortunately it is not possible to reliably differentiate the eggs of F. hepatica and F. buski by morphology alone.
The below image from this case clearly shows where the operculum (lid) was located. I often find it difficult to see the operculum on Fasciola/Fasciolopsis eggs since the operculum does not have shoulders and often blends in smoothly with the wall of the eggs. One trick to expose the operculum is to gently press on the coverslip and 'pop' the operculum open!
In the second part of this case, I posed the question of what the structure within the 3rd image is. What I should have told you is that the photos from this case were taken from eggs that had been incubated. Eggs of Fasciola/Fasciolopsis are shed from humans in an unembryated state and no definitive internal structures can be seen. However, after being released into fresh water, the embryo matures into a ciliated form called a miracidium. Arthur gave a nice description in his comment.