Hi, the next update is scheduled for the end of this month should all things go as planned (we were stuck with hotixes for a little longer than we expected, so there's always a chance the update might be pushed to early June).
The update is scheduled to contain the bulk of the features appearing on our Trello roadmap. Exact date should be announced in the coming week!
Like others have said, you breed the mini aviary animals directly in the building. That being said, I'm working on fixing the issue where the aviaries and nurseries are reset after loading the save, and the fix should be out pretty soon!