According to your description it seems to be a compatibility issue. I suggest you to verify if you are using the latest drivers for the
Microsoft Wireless Comfort 5000 keyboard and Mouse, select Windows® 10, 64bit
NexStar Hard Drive Dock documentation talks about compatibility with Windows® XP, Vista , 7 and 8. It is necessary to confirm with the manufacturer if there is any diver available for Windows® 10.
I suggest you to narrow down the issue. Unplug all USB devices from the NUC; then, plug the keyboard and mouse to the NUC, install the latest Microsoft® driver and check if you are getting any error message in device manager. Make sure you already have the BIOS version 0354 and latest Chipset, Me and USB3.0 drivers.
Then, plug one by one USB devices to the NUC and check if it is recognized properly by the NUC. If not, check if USB device manufacturer has a newer driver or firmware.