The Parallels networking mode was “Shared.” Switching the mode to “Default Adopter (Bridged)” solved all the problems. Now, the MM Server can be seen from both my Network Player and Blu-ray Disc Player, which are functioning correctly as I expected.
Under MM’s Media Servers, only “NAS: LinkStation: PVConnect: Windows Media Connect” is seen. Not displaying the “MediaMonkey Server” here is fine, I think. I do not know why “:PV Connect: Windows Media Connect” shows this time though.
Thank you all for the help!!!