Hi and welcome to the forum
Australian finches are regularly referred to as grass finches, due to their habit of feeding on green grass seeds when they are available. The green grass seeds will encourage your birds to start breeding and provides them with a nutritious meal.
The following link has information about growing grass seeds for your birds.
viewtopic.php?f=84&t=21732&p=188305#p188305
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Finches should have a good dry seed mix, cuttlebone, mineral grit, clean water and green feed every day. Green feed can be dark green leafy vegetables like spinach or silverbeet. They will also pick at different fruits and veges. Just make sure any food you give them is clean and free of chemicals (pesticide/ herbicide).
Avoid feeding onions and onion relatives (spring onion, leeks, shallots, garlic), and no potatoes.
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You can feed your birds on soaked or sprouted seeds. I prefer sprouted. Soaked seeds are simply dry bird seed that is soaked in a container of tap water over night. The seed take on water and swell up a bit. After 12-24 hours of soaking, you put the seed in a sieve and rinse it well under tap water. Drain the water off and feed it to the birds.
If you get soaked seed and put it in a plastic bag and seal it up (ziplock bags are good for this), you can leave it in a warm place (on top of a fridge) for a day or two and the seed will germinate and little roots appear from the seed. When that happens, put the seed in a sieve and rinse it under tap water again, then drain and feed to the birds.
You can feed soaked and sprouted seeds every day if possible. It is used as a supplement to their main base diet, which is above.
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You can make egg biscuit mix for your birds and it will help provide them with protein and other nutrients.
Hard boil a chicken egg for 10 minutes.
While the eggs is boiling, get a cup of cornflakes and put them in a paper or plastic bag and put the bag on a table. Use a rolling pin to crush the cornflakes into tiny little pieces.
Peel the egg shell off the egg and crush the shell up and put it in the garden or feed it to the birds.
Put the boiled egg in a bowl and use a fork to crush it up. Then add the cornflakes and mix the egg and cornflakes together.
Put the bowl of egg and cornflake mix in the cage for the birds.
Remove the egg biscuit mix at the end of the day so it doesn't spoil and attract ants.
Egg biscuit mix can be fed every day as a supplement to their base diet.
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Have 2 nests for every pair of birds you have. Make sure the nests are all the same height and are about 6 inches below the roof.
Add lots of green and dry grass to the cage/ aviary so the birds can use it to build their nests.
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If you have a dog, train it to look at but not touch the birds. And encourage it to chase cats away from the birds.
If you don't have a dog, get a cat trap (live animal trap) and have it set 24/7 near the aviary to catch any unwanted cats coming onto your property to attack your birds.
If you have a pet cat, try to discourage it from going near the birds and make sure it is sterilised and indoors at night so it doesn't scare the birds during the night. Get a cat trap even if you have a cat, so you can catch unwanted cats wandering onto your property and killing your birds at night.
Put a padlock and chain on your aviary door to stop people stealing your birds or leaving the door open so your birds fly away.
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Make sure the birds are in a dry draught free enclosure and keep cold wind and rain off them.