The reactor is not Egg like. It is the Containment area that is egg like, So no steam or nuclear radiation cannot escape.
It depends what size the pods are. And I assume you meant there is "something alive inside" of EACH pod. If they are the size of chicken eggs, then it's most likely a clutch of alligator eggs. They dig a hole near water and lay their eggs in it, then bury them.
If the betta is a male, it is probably a bubblenest. Happy males often blow them in captivity in an imitation of their wild behavior (blow and maintain a nest on the off chance a female might appear and be impressed). If it is a female, probably eggs. Well fed females in good conditions will fill with eggs. If not able to breed (there is no male to breed with) they will lay the eggs to get rid of them. If she cannot or does not do this she may become eggbound; this can be fatal. You should try to feed her less, and especially cut down on the protein.