The 5711 switched over to the newer version of the 324, the 26-330, back in late 2018/early 2019. I would assume any upgrade to the 5711 would come with the newer movement as well.
This is incorrect. Feel free to bring in your 5167A to any AD and request the bracelet. Retail price is $3720 and will include the bracelet, 2 spring bars and the 2 attachment links.
That can be changed in the current collection with the blessing of Patek is the 5167A. The bracelet and strap are made to be interchangeable and you can actually order the bracelet if you have a strap version from Patek.