Congratulations to everyone who wrote in - you all got it right.
1. Identification? Ascaris lumbricoides
2. Explain the difference between the 3 eggs (i.e. why do they look different even though they are from the same organism)?
The top egg is fertile.
The middle egg is infertile. Infertile eggs are larger and longer than the fertile eggs, often have a thinner wall, and can take on bizarre shapes.
The bottom egg is decorticated - it has lost it's outer mamillated layer. Importantly, note that it still has it's characteristic thick wall. This allows its differentiation from thin walled hookworm eggs.
As a bonus, here is an extra photograph: The fleshy 'lips'/mouth parts of Ascaris. You'll notice that the mouth does not have any 'teeth', hooklets, or cutting plates. That is because, unlike Strongyloides stercoralis, Trichuris trichiura, the hookworms, and the tapeworms, Ascaris lumbricoides does not attach to the mucosal surface, but lives freely in the gut lumen.