Will this motherboard work with Intel Quick Sync?

You will need a monitor with a spare DVI-D or VGA port since the mobo only has those connections,connecting a cable from the mobo to the monitor will enable the use of qsv.
You could fake this connection on windows 8 but I don't know if it's possible on win 10.
 
No they won't except for some games that let you select a GPU from the settings.
The word spare suggests that you would keep your GPU connected and also connect the mobo to the monitor,you can switch inputs on your monitor if you need to see the iGPU or the real GPU but almost exclusively you would only have the GPU selected.
That way both GPUs will be available to the OS.