Specific URL routing
Summary
I think you just need a couple of different views to create most of the functionality, but because the continent paths do not leave space for a path argument to call the view (eg example.com/viewname/africa/...), you might need to either duplicate the view with several displays or use some .htaccess mod_rewrites to point continent names at the view.
I have inserted a + into the first path (I hope that is alright?)
Suggestions
view: terms_by_continent

http://example.com/africa/news+politics
http://example.com/europe/reviews
http://example.com/antarctica

are presented by a view called terms_by_continent, with a contextual filter on term:name, accepting multiple arguments and defaulting to 'show all'. Create a different 'page' display for each continent so you can change the path to simply, for example, africa
view: terms_by_category

http://example.com/news/politics

would be a view called terms_by_category. The namespace is a bit difficult here because, unlike continents, I would guess this vocabulary might be subject to change, so creating multiple views displays would be tiresome and prone to error. If you are able to insert another path component then this becomes easy, ie category/news/politics would be served by a view of nodes with a contextual filter as above.
Multiple terms would normally be seperated with a + or similar, but if you needed to use / (ie news/politics) you could do a mod_rewrite on category/* to make this presentable
If you could not afford to add the category path component then I would guess you are stuck with using views displays as in term_by_continent to claim the paths that match each of your terms, accepting arguments for additional terms.
node: custom path
Finally:

http://example.com/2013/12/17/conflict-in-kongo-continues

This is the actual path to a specific article (node), so path auto is definitely the way to go. It will allow you to use tokens to construct your path for the appropriate content type, using date components and title.
Other solutions
I had a couple of other suggestions:

look at page manager, which might allow you to have greater control over paths for your views
you could try using pathauto for terms as well as nodes, and then replacing the term display with a view that accepted term:name as argument (as above), You could do this using term display or tvi

For option 2, I believe that (assuming there is not an existing page with this path), africa/news/politics for example, would not find a match, so would look for africa/news. Because that path also does not exist, it would fallback to africa, which (thanks to pathauto) takes you to the africa taxonomy term.
The term page contains a view, which accepts arguments (ie news/politics) and therefore you should get the appropriate listing. The view might need several displays which accept increasing numbers of arguments in order to allow the '/' seperated arguments, ie view/%,view/%/%, view/%/%/%