I don't want to hijack this from Greg, but I want to chime in too.
1. PiCore player is just the player which outputs sound to a speaker/audio system
Yes.
2. The sound files to be played are sitting on a seperate server box running LMS
Yes.
And the LMS server is also able to stream internet radio stations. Something I use it for the most.
The biggest advantage of LMS compared to other music (or multi-media) servers is that is able to synchronize the audio on two or more players.
That makes it the only low-budget alternative to a Sonos system, as far as I know.
3. LMS can be downloaded from http://downloads.slimdevices.com/nightly. At this URL there is just a downlaoder named "logitechmediaserver_7.9.0~1452060863_all.deb"
and not the actual .deb file. I have (Debian 8 running on another box) I was not able to install LMS.
Have look at my tutorial, it describes how to install squeezelite and an LMS server on a Raspberry Pi:
http://www.gerrelt.nl/RaspberryPi/wordpress/tutorial-stand-alone-squeezebox-server-and-player-for-bbq/BUT PLEASE NOTE: The tutorial is in need of a revision. I've changed my squeezelite installation tutorial to use Raspbian Jessie, but this tutorial still needs Raspbian Wheezy.
So, if you only plan to use the LMS part of the tutorial, you're fine. As long as you use Raspbian Wheezy.
A piCorePlayer should be able to connect to a LMS server running on Raspbian Wheezy without any problems.
Is there another server to replace LMS?
F.i. VLC or similar?
Not that I know off.
4. Is there a streaming server availabe for piCore (piCorePlayer OS) ?
As piCorePlayer is a Squeezelite based player, it can only connect to a LMS server.
But please correct me if I am wrong piCorePlayer-people!
Greetings,
Gerrelt.