Sorry for the late response, I wanted to acquire proof before I answer your question.
As for the "are they eggs question." I don't think so, Sea apples (P. violaceus) are broadcast spawners; the males shoot sperm into the water, and the females follow afterwards with their eggs. Once the eggs and sperm meet in the water column, the fertilized eggs are formed and become a part of what we call zooplankton. The reason I'm saying i don't think so, instead of a definite no, is because I couldn't find information on how they store their eggs pre-release. -->
https://www.researchgate.net/profil..._Sri_Lanka/links/54acdf4f0cf2479c2ee85536.pdf
Now for the bumps:
In the black, dotted box: This may be what you're talking about. In this case, I'm not sure what that is. Seems like an abnormal growth, but you have to remember that I still have limited experience with sea apples.
In the red, closed box: Those are its tube feet.
Green, poorly drawn triangle: Those are random bumps they have. Don't know their purpose, but it is completely normal.