In regards to your media player, it is possible to do it without the use of Windows Media Player. You could use the Microsoft Multimedia Control 6.0 that can be referenced through Visual Basic 6.0 by going to Project > Components and checking 'Microsoft Multimedia Control 6.0'.
Whiteboard is easy. Drawing on a PictureBox can be done with either GDI or simple SetPixel APIs, etc.
To do that over the net you would just send the x,y coordinates to the other person. And of course any other info along with it like current brush color, brush size, etc. You'd probably want to use Winsock for this.
I might be able to make a small example later on if I have time, but there are a lot of them on the net already.