"What happens to my printer/external hard drive/external cd...as they are all connected to the laptop"
Nothing, just continue using them as you normally do.
"And is the idea to be running laptop off the battery?Or should I plug in the power supply wherever I take it?"
You can do either as you wish, so long as the battery is charged.
"Any other tips or warnings as I venture into the Wireless World??"
Just make sure that you have wireless security set up on the router, choose the WPA-PSK option in the settings. Check out the router's manual on how to set that up.