Does Apple want the trade-in iMac power cord returned with the iMac?

Also, please remember to properly prepare the trade-in iMac per What to do before selling or giving away your Mac

Yes, they want the power cord and of course the iMac. You can keep your keyboard and mouse.

What do I do with the power cord and keyboard?

They do not want the keyboard or the mouse. They did not tell us what they do with the power cord, however my guess is they are re-used after they are refurbished.