Computer Networks, Wireless Networks (Muddiest Points)

Can computers or laptops with differing operating systems(for instance Windows or MAC) be able to access each other or share the same LAN?
Is internet connection needed for computer users on a LAN  to communicate with each other or to share something?
How does one secure a computer network from viruses or hackers? I was reading that hackers could administer viruses to every computer connected to a network.