Hi, I use to have cockatiels. Infact I grew up with them. My dad was a big fan of birds, and it passed down to me. But now i have ferrets, so no more birds for now.
I had two females that use to lay unfertile eggs. They were both around 5-6 years when they started laying them. Some start the minute they are mature enough while other may start after a few years of having them. According to books that I have read, this isn't uncommon. Some females lay unfertile eggs, and usually its every 6 months, one egg every other day. Some birds lay 3 eggs while other can lay up to 6. The important thing to worry about is egg binding! Thats why your vet reccommended mineral blocks and cuddle bones. I also recommend vitamen supplements for your bird!
Egg binding is when the egg dosn't pass through the canal and gets stuck and can crack in thier body and can lead to death if it dosn't come out. As for the laying of eggs, the one book I read said you should leave the eggs in the cage for about a week or two and then take them away, if you take the eggs away to soon, they might try to replace the eggs and could die doing so. Also, you could replace the real eggs with fake ones (try craft stores). If you have a male bird with your female, and you think they may be fertile eggs, you can always poke holes at both ends of the egg and blow the yolk out to prevent any unwanted babies. I don't recommend not to breed cockatiels unless you know what your doing, have the proper tools and have talked to a vet!
It isn't uncommon for them to hang around thier eggs and sit on them for hours, they usually share the work with thier male partners. Usually they don't set on them for long hours untill the last egg is layed untill then, they may just lay the eggs and pay no attention to them.