Reflowing the board is a waste of time. You can't fix a bad GPU by getting it reflow. you need to replace it. By the age of the computer i feel like is better for you invest in a new macbook. Because that computer had a known GPU issue but apple end the GPU recall on that model already. Good luck!
Hi, The bottom case of the macbook already have your serial number. If you buy a third party bottom case it will either come with a random serial number or with no serial number. Hope this help. Good Luck!