RE
Ok, that's what I did...
I don't know if there's a bug then or if there was something wrong left, but after that when I get the checkout page, if I check the same as billing address checkbox and leave the shipping address empty, it doesn't copy the informations... the next page doesn't get the shipping informations, neither Paypal...
Also, I was never able to make the Paypal button at the top of the checkout page to work. I had to remove it. It always pointed me to the pp_checkout_failure.php page...