So, I find it a bit strange that I there's not many websites etc about zebra finch vocalisation. Even though they are a intensely examined species, thanks to the easy breeding.
I have two little hens, living freely in my room, and it's just incredible how many different sounds they can make. Not to mention you can hear the obvious difference between every single bird, they all have their own unique voice, and way to "beep".(and they have their own personalities as well, their own way of sleeping, bathing, beeping, etc.)
The most recognisable sounds are the :
simple, chat like beeping
the loud morning beeps- both of them have their own rythm etc
the "come ,there's some food here"
the "this is a good place to nest, look at this nesting material"
the squatting squeaking"I'm ready to mate"
the mating squeaks,
the confused "what's this?" chirps
and the sound they make when they're dancing
Here's some simple beeps and the nesting squeaks from my Finchy(they are building a nest on my lamp...Couldn't stop them.haha) https://youtu.be/GNe3Jg-k-mE?t=27
https://www.youtube.com/watch?v=ogRKauxHX-M
This is Swan's(the white finch) version of that sound : https://www.youtube.com/watch?v=HugvL7v609U
Also these little sneezing sound Swan(my white zebra finch) makes when she's bathing

https://www.youtube.com/watch?v=l0O7g29ghKg&t=1s