Mine have laid eggs twice now, in a pot just like yours. male pink con, female black con, the male guards the eggs, and after a day or so they have disappeared, I guess he ate them. Now I don't really care, I don't have them in hopes of having a zillion babies, it would be cool, but whatever, but if you do, i'd take out the male, if he is guarding the eggs like mine was doing.
Yes, the parents should be well kept and stress free. You should remove the fry once they reach about 1/3 of an inch or so to avoid being eaten by their parents. Convicts are the easiest to breed with some hardy fry's also, but they fry's do take some time to grow.