When displaying a taxonomy term, how can I also display the teasers of all the child terms of the current term? I still want to display all the content and fields of the current node, but also display the child teasers.
The taxonomy display won't do this on its own. You could create a view to do this, then display the view below the term page.
If you call the view from a taxonomy term template you could use a "Contextual filter" to pass the term id (tid).