If you sign in to a Windows 10 pc by using a Microsoft account. e.g. email@example.com , then you can connect with remote desktop to this pc, by using the user name: microsoftaccount\firstname.lastname@example.org.
On my home network I wanted to set up a Remote Desktop connection to a Windows 10 machine from a Windows 8.1 machine, by using the credentials of a Microsoft account. Both machines were using the same Microsoft account to login.
Turns out I had 2 problems, first on the Windows 10 machine I had not turned on sharing.
When I went to Control Panel\Homegroup, on the right of the screen a text appeared to enabled sharing, when I clicked OK, I could connect with Remote Desktop to the machine, but then I had to enter credentials.
Assuming my email address, used to login with my a Microsoft Account is: email@example.com then you should enter the username as: MicrosoftAccount\firstname.lastname@example.org
Yes you really have to put the text “MicrosoftAccount” in front of the email address.
I was using Microsoft Remote Desktop on a Microsoft Windows 7 machine to remotely control an other Windows 7 machine an I was running Skype on the remote machine. There was coming sound through the boxes of the local machine, but the microphone was not recorded even when the settings of the Local Resources where: Remote audio playback [Play on this computer] and Remote audio recording [Record from this computer].
The problem was found in the control panel > sound > recording > Select a recording device below to modify its settings:
this list was empty.
After setting the registry key [HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Terminal Server\WinStations\RDP-Tcp\fDisableAudioCapture] to  on the remote machine and reconnecting the problem was solved.