If you want to connect to a minecraft server on the PC you will need some sort of internet connection to connect to the server.
On the Xbox, you will need internet,as well as a Gold Subscription, to invite others to your map or join someone else's map
On mobile devices, you must connect them both to the same WiFi network to play together on a world
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No, you do not need wi-fi.
you have to use wifi
You need to download an emulator that supports wifi
no
No. A WiFi Router is not needed to use a WiFi USB adapter. You just need the internet and a compatible PC/Laptop like Windows XP / Vista. Just plug the USB in while you have the internet running and you are on WiFi.