Contextual Filters via Taxonomy
Contextual filters are just the term. So in the contextual filter input box for the Views Admin you would put mississippi-river as an example. In addition to Term name converted to Term ID you want to be sure you check the box for convert spaces to dashes further down in the specify validation criteria or else "mississippi-river" will not be found because it's expecting a space and you're providing a dash.

For the parent/child filters you're trying to achieve look at Taxonomy Edge. The -dev release contains some contextual filters for "parents" and "children" of stuff.