Do I have to reset it up on this desktop?
Yes. Modem needs to be rebooted. Then the router.
You do this by powering each device down and then restarting in turn when the lights come on.
Will I need the ethernet cable to remain connected?
Not if you want to run the desktop wirelessly - but I don't see why you would need to [run it wirelessly]. Wired is faster, more secure and more reliable for your desktop.
Filesharing is easy. Just run the wireless setup wizard. It will handle it.
Put the printer drivers on the laptop so you can use it through the network.