SqueezeBoxes would give you ultra-easy access to internet radio (they are quite good at it), but not playing different things in different room unless you have more than one computer, in which case you can bind different players/source.

For both your needs, I would take iTunes/iPhone out of the picture completely (no internet streaming worth mentioning and it is painful to setup multiple iTunes with the same music to play different things at the same time).

See Mojo's signature