Can you use a wireless mouse for notebook and desktop computing and if this is correct why would I do this ie battery life recharging over direct connect?
A wireless mouse can be used for both. As for recharging, most
wireless mice you will look at take Alkaline batteries, so you have
to replace them when they die. If the mouse contains Rechargable
batteries, then yes it will have to be plugged into the PC (or
wall) to charge.