To answer your questions (again) completely:
Yes, you can return things to Nike stores without a receipt.
No, they do not have to be things that are sold at that particular store.
Yes, they have to be new/unused OR have some sort of defect with them AND have to be within 2 years of production (you MIGHT get away with it in-store if they are older than 2 years, but I definitely wouldn't send stuff back to NDC if it's older than 2 years). As far as having the original box... I don't think they care that much usually.
You will receive store credit (a gift card) equal to the value of the current selling price of the item at THAT particular store (these prices can be/are different at different stores).
You will need to have your driver's license (or have someone with you who has a driver's license). This applies no matter what if you don't have a receipt... whether you are going for store credit/gift card/exchange/different size/etc.
As far as I know, you can exchange AT LEAST 3 different times with the same driver's license up to AT LEAST around $500 in store credit (these are figures that are not confirmed, but have come from my experiences/research of doing this).