Ford's giving you UP TO $3000 on your junker - but you have to have had it licensed/insured for 6 months I think...maybe you qualify. (see article on front pg of main site)
$500 starting trade, but if your car is worth less than $0, then you'll get the $500, but have less room on the price. Either way, you get nothing for such a trade.
Actually the amount you receive under that program just depends on what you are buying, not on the actual value. For example, buy a Fiesta and get $500; buy an F-350 and get $3000.
But yes, there are requirements for registration, names must match, etc.