yes this works with the MK850 - the MK850 has the option of Bluetooth as well as the unifiying receiver.

I assume it should also work for this keyboard and mouse. I myself have a different Logitech keyboard and also had quite a few problems installing the UE. In the end, downloading and installing Driver Easy (free version) helped. The scan detected the UE as a "device with missing driver" and then led me to the correct driver installation. After that, it worked for me in any case.