The website ePals has a great reputation for working with teachers to meet the first two challenges, offering great ways to find teachers and classes to connect with all over the world. Since making its own connection with National Geographic last year, ePals now has the third covered, too.
Project topics range from cultural studies to habitats to maps (a natural for National Geographic). You can search for a class on ePals and choose a project together, or choose a project and then search for a class on ePals. The site offers built-in translation of Chinese, French, German, Italian, Japanese, Portuguese, Korean, and Spanish for classes that need it.
Great way to add a global dimension to your teaching. Find out more about getting started here.
And (did I mention?), it's free!