As I know NUC7 is using the latest hardware and it does not support Windows7 OS. If you really want to install Win7 on NUC7, you can go to MSI or ASUS website and download a Win7 iso tool, which can add the USB3.0 and NVMe drivers to your original Win7 iso, after you burn the modified iso to your USB disk, you will be able to use it to install Win7 and your USB keyboard & mouth will work normally.
Again, I suggest you not to install Win7 because Microsoft stopped support for Win7 for kabylake platform, and the system will frequently show warning window on your desktop which says: Your hardware is designed for newer OS... blabla... or something like that. And Microsoft will not push hot-fixes to your Win7 until you update you OS to Win10.
This message was posted on behalf of Intel Corporation
That’s right Windows® 7 was not validated by Intel for this NUC, the operating system that is validated and recommended to install is Windows® 10.
The reasons why the mouse and keyboard does not work when you try to install Windows® 7 is because Windows® 7 comes with USB 2.0 and this unit only has USB 3.0.
If for some reason you need to install Windows® 7 you can try to follow the steps at the following link and see if it works: