Not quite... they need power sources of their own, but almost all nanocomputers have built-in chlorophyll-mimic solar panelling to provide the electricity they need. In some cases, though, they can be fitted with outside power sources, but this is generally only for extremely intensive jobs and would not be a necessity for a nanocomputer such as mine.

[Robert nods to himself at the next part.] Yes, all nanocomputers store information in quantum bit states - known as qubits. The capacity to store information varies between nanocomputers, with simpler ones generally having less. It depends moreso on what one wishes to employ the nanocomputer for.

As for the Internet itself... much of it is a wireless network capable of sending and receiving information of many forms; many of the major hubs for it are built into the cities of Terra. Linden - my own city - for example, has a prominent Internet hub in the city's commercial core. But there are smaller hubs scattered throughout the planet, wherever it is not inconvenient for the environment - not that the hub units are particularly large or destructive, and they have been being refined in recent years, but there is still much to be cautious about.