Welcome to the forums!
I'm sorry for your female budgie's passing... when it comes to disabled birds or birds born with birth defects it's advisable to not breed with them to avoid deterioration of their health and to prevent the chance of chicks inheriting the disability.
As far as the eggs go, it takes a keen and experienced eye to spot when an egg is infertile or fertile without using candling. And to judge that from a photo (which is hard, nothing beats actually seeing them for real), unless the quality and lighting are perfect it's not possible to give an accurate guess.
Still, I will try to explain the differences to the best of my abilities.
All eggs recently laid (as in from a few hours to one full day) will have an overall light pink tone to them. After a few days of full incubation, a fertile egg will change from the pinkish tone to a very solid white colour. Infertile eggs will have some of the pinkish hue and also have more of a translucent white colour, the white won't be so strong as the one from the fertile egg.
An egg gone bad will have a greyish looking appearance, and it should be taken away from the nest, the same goes for eggs that will have a blood ring across, meaning the developing chick died in the egg.
Eggs take on average 18 days to hatch but they can take up to 21 days depending on the time the hen started to fully incubate them.
I see from the photos that you have 3 budgies on a cage. When it comes to breeding it's best to have just the pair in a cage without any other bird to possibly meddle with things.
There is a lot of info on the stickies here at this section of Talk Budgies and if you haven't done so already, do check them out.
Good luck with your pair and their eggs!