Quote from Corsair 800D features:
"Three 140mm fans included, with the ability to add four more 120mm fans"
Those are 120mm x 3 on top and I would consider premium quiet fans like Noctua's
Yes that is the correct cable for the fans and I would connect them to the PSU before using the mobo connections, it's cleaner looking and keeps un-needed power from flowing through mobo. Another reason to use Noctua's as they are provided with speed resistors but I've found even wide open they are dead silent.