9 times out of 10, customs wont know the difference (their computers dont give them all of the information of the vehicle). All that said, get your brother to write you a little note, just in case. You could run into trouble if you get pulled over at any point, or if everything doesn't go perfrctly smoothly, through customs.
Yes you most certainly do. Otherwise you could be at worst detained on suspicion of trafficking in stolen goods and at best refused entry.
It would be a good idea to carry the paperwork with you. I would also make sure it has his contact info on it for border officials.
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