Does Creator CI20 support these details?
NO, which single-board-computer of your portfolio supports?
The hardware on the Ci20 does support the details you mention. Details on the software support below
• Playing MPEG-2 transport streams
Yes. But on Debian 7 images using Kernel 3.0.8. And Using .
• Playing of MP4-files with h.264 encoding Yes. But on Debian 7 images using Kernel 3.0.8. And Using 
• Video reception through multicast
Do you mean receiving video from ethernet packets? Should be fine as that would be a linux kernel thing. And ethernet works.
The latest Debian 8 image is better in several aspects but doesn’t support HW accelerated video playback yet.
Also, please keep in mind. Hardware accelerated video playback support in Debian 7 is beta.