Some progress!
Windows 10: I uninstalled KB3194798, rebooted and both the date-picker icon and the rules are visible. I am however, being prompted to install .NET 3.5 every time I look at the rules and I am unable to do so (I get an error 0x800F081F).
Windows Server 2012: I uninstalled KB3192392, rebooted, no change. I then uninstalled KB3185331, rebooted, success. Both issues are gone and am not being prompted for .NET.
So for the time being, I'm OK.