Every time I expand a particular container (e.g. computer group, filter package), all the other containers that were expanded before are automatically collapsed. Why is that, and can I disable that?

You can configure this behaviour in Tools -> Options by setting or clearing the Automatically collapse unselected groups check box.

By default, only one container at any given level in the tree is expanded at the same time. This is to help keep the interface clean, but you can disable this option.