Wireless mouse or keyboard can be infrared or Bluetooth style, which is a direct one to one connection
Wi-Fi is on a different frequency and setup differently
Wi-Fi usually has a central access called a router, and is setup up as a network, but in some cases a direct connection between two devices can be made
Internet access is not needed, for a pc to connect to a printer
Unless they are not in the same location, ie send something to the printer at home when on the road..not something usually needed