What is the altitude one must reach in order to communicate with the ground? Is it possible to talk to ground via radio flying over the oceans? How to know the exact position of an aircraft over the oceans?
As Ron mentions in the comments aircraft flying transatlantic routes (or really any long route for that matter) may use HF radios operating in the 3-30MHz range to communicate over long distances. HF radio waves have the ability to "skip" off the ionosphere if directed properly and thus propagate over the horizon and beyond line of site.
You can also find a lot of good info here under the "communication" tab.
As for knowing the exact position of the an aircraft, this answers covers most navigation methods out there.