Cabling
Well if your talking about something like Skype its the internet. But mostly if your talking about computer sharing info its a programm downloaded on both computers.
wan
network
Internet is the source to view internet stuff.
connectivity.
its a computer network
Computers can be used share data and software. It can be done via various other 3rd party applications.
Wi-Fi Modem.
Yahoo, Google, etc.
LAN ( Local Area Network )
A 4-port WiFi router is just a router that has four WIRED ethernet ports in addition to its WIRELESS 802.11 interface. This would allow you to share a single WIRED internet connection between 4 computers using ethernet cables, in addition to many other computers using the WiFi interface and no cables.
Most likely, yes. If both computers are running Windows, for instance, either should be able to share its printer with the other. However, both computers would have to be running in order for the share to work.