In any case, I find it hard to imagine the use of "egg" in the singular. The only case that comes to mind where "egg" might be in the singular form is that in which we refer to the word "egg" (metalinguistic use of the word).
I agree with you, Gustavo, that we generally use "egg" as a count noun, and that "eggs" (plural) is probably a better choice for Jiho in (b). As a vegetarian who doesn't eat eggs, or who tries his best not to, I am accustomed to using "egg," occasionally, as a noncount noun.
Thus, if I am placing an order for food at a restaurant I have never eaten at before, I will often ask whether a particular dish is made with eggs (count noun), but occasionally I will ask, instead, whether it contains any egg (noncount noun). I can't recall having ever thought about the grammar of it before.
Jiho's use of "egg" as a noncount noun in (b) -- "The next thing on the list is egg" -- brings to my mind liquified eggs, which pour out as a single fluid. If I'm not mistaken, the fluid formed from liquified eggs is sold in cartons in many grocery stores. If I put that stuff on my shopping list, I might refer to it as "egg."