B. Why I can’t see all the current song/programme info, only part of it? Or why is the current displayed programme info not refreshing?

Not all song information is displayed:
This depends on more factors. First of all the DAB radio tower needs to send this information and some radios might only be test radio channels with limited info. The DAB+G receives all this, and with the Gateway it sends all the information to the car head unit. It will depend on the car head unit that how many lines will be displayed. In the worst case only the radio name will be visible, maybe the song name too. In the best case more information will be there like: artist, album and in case of the radio programme also some info of the current programme (for example the phone number for that radio show).
The displayed DAB radio name and information are not refreshing:
Unfortunately some car head units are not refreshing the display that frequently. Some cases not at all, only when you start the car, or in other cases you need to go to the previous menu, then go back to the music menu and that refreshes the info. If the car works like this, then from the side of the DAB+G this can’t be affected unfortunately.