If I want to make a site that lets users refer other people to the site to complete offers and make money. Can I tell the gov't I pay them all my earnings from this so I don't have to pay taxes?
Sure you can, you just have to get all their social security numbers, have them fill out a W-9 and send them a 1099 at the end of the year. Of course, you really have to pay them also.
Sure you can, but tell me this what color jumper do you prefer, orange or do you like the classic black and white stripes???
Yes you will need to keep tax records for all your users if they make more than $600 in a year, if they go over this amount don't send them their money/prize/whatever until they return a 1099 to you, otherwise you'll never hear from them again and you'll end up having to pay for it.