Fertility is a much discussed topic, here I will try to answer some of those questions.
There are many reasons for infertility in birds which I hope to explain, some reasons you might already know and some you may not. Birds, just like humans, can be sterile and never produce offspring. It is not gender-specific, so it could be the cock bird or the hen who is sterile. The reason for either or both being sterile could be genetic, poor nutrition when developing as a chick, wrong/erratic temperature during incubation, underdeveloped or missing reproduction organs, lack of natural daylight, viral, genetic, age, bacterial or fungal infection.
If you are finding all the eggs produced to be infertile then look at the age of each bird, when in old age hens naturally stop producing eggs and often the cock birds do not copulate properly. Sometimes you might find you have two hens thinking you have a pair (cock and hen) or two cock birds thinking they are a pair (refer to Gender section for sexing gouldian finches). Any signs of development within the egg/s will tell you that both male and female are fertile. If the embryo dies at any stage it will not be down to infertility but rather an incubation problem, (refer to Breeding section for incubation problems). Sometimes the hen may never lay an egg in her entire life which usually means she is infertile and some hens just simply never want to breed.
Please note: Hens can lay eggs without the presence of a cock bird, and all eggs laid will be infertile. Although you may have a true pair, the hen may still produce eggs even if there has been no copulation from the male. Sometimes you may witness copulation and no eggs are ever produced, but this can be because the hen may not be in breeding condition. Sometimes the hen will lay eggs and the eggs are eaten, eggs that are eaten are usually by birds lacking in calcium, a vitamin, protein or other mineral. By the time you notice there is no egg there will be nothing left, no shells, no yolk, nothing! And believe no eggs were ever laid. If you set up a nesting box camera, you can learn a lot about what is happening in the nest away from the human eye.
If you believe both male and female are reasonably young and are in breeding condition but never produce any eggs you can work by process of elimination by paring the male with a known fertile hen and pair the hen with a known fertile cock bird, let them breed, wait for the eggs and candle the eggs to check for fertility. It is possible that by pairing the male and female with other known fertile birds that both produce fertile eggs with their new partners, this could be down to poor copulation or the birds simply not really breeding but the hen still laying eggs. If you do pair each with new birds to test for fertility, then make sure both pairs are housed in pairs with no possible interaction from other birds, or the test becomes void. If when paired with new partners (during the test) one never produces fertile offspring then you have found the infertile bird.
You should be kind and throw away her eggs if they are laid infertile and replace with a fertile egg from another pair who has laid an egg that day, so the parents can experience parenthood too. Each day as she lays an egg test for fertility, if infertile then toss it away, go to another nest and take a freshly laid fertile egg and put it into the infertile bird's nest. Next day do the same but take an egg from a different nest each time. You might want to put a dot on the fertile eggs using a pen for easy identification, those eggs without a dot will be a newly laid infertile egg which can be swapped.
Although you might have a bird which is infertile, the pair can still successfully raise chicks from other gouldian finches, thus making feeding easier for the other breeding pairs by them not having to feed too many chicks at once. It is a lot easier for a pair to raise 4 chicks than 5 and save the parents from a lot of stress. I have raised many chicks from the day they hatched until way past fledgling stage, even if you are raising a single bird it can be stressful with the constant begging. Gouldian finches do not like to foster chicks from other nests, but will foster eggs quite happily if they believe the eggs are their own.
I have never found any product to really work to help with poor fertility, even though there are lots of products out there. I do not believe supplements can cure infertility, despite there being lots of products that claim they can. If there is an infertility problem, then I'd start with the above process of elimination by finding out which is the infertile bird. As long as the breeding pair have a balanced diet including minerals, protein and calcium, then I am sure you can rule out supplements for infertility. Follow a good breeding program which would also cover diet and almost nothing can go wrong.
If the bird is kept too cold or too hot for lengths of time, this can have an effect on their fertility. Being stressed for long periods of time or persistent stress factors will also affect the bird's fertility. If the bird has a hormone imbalance or defect, then this could also have an impact on their fertility. Humidity is another consideration because if it is too humid for a long time then infertility may be a result. Illness, infections are also other possibilities.
Most hybrids are infertile because of their chromosomes, they cannot produce viable gametes which prevent natural pairing on a cellular level meaning their sex cells are not viable. In reality there are too many reasons why a bird could be infertile, far too many to list, but this page will give you some good ideas of what may be the cause of any infertility in your birds.
Shining a light through the eggs can reveal if the egg is fertile or not which is called 'Candling', eggs that have a dull yellow appearance are usually infertile and even those with a nice strong bright yellow appearance can still be infertile. In the Charts section you can find a chart to compare your eggs to see if they are fertile or infertile or even at what stage of development they are at. Infertile eggs should be discarded right away to avoid spreading any bacterial infections to other eggs within the nest.