There are a number of people around the world who in some way conduct research into the behavior or biology of zebra finches. A few of these people have web pages you can look at, but please DO NOT contact them with questions about your pet zebra finches - that is not what they are there for. (Go here in stead.)
A number of pages have general information about Zebra Finches, as wild birds or as laboratory animals. I suggest you use Dave Runciman's Zebra Finch Page as a starting point:
The Zebra Finch Page by Dave Runciman, Australia
The Zebra Finch: a Synthesis of Field and Laboratory Studies, (Abstract) by Richard A. Zann
By studying Zebra Finch song, scientists hope to learn more about the social effects and causes of Zebra Finch song, as well about learning in general.
The Zebra Finch Song Archive by Heather Williams, USA
Birds sing in their sleep, BBC News, October 2000
Studying Zebra Finch physiology can not only help us understand Zebra Finches, but also give insight into other areas, such as the effects of drugs, etc.
Mechanism of Sperm Competition in Birds, Abstract for an article by Tim R. Birkhead published in American Scientist May-June 1996