That’s entirely expected behaviour.
To change channel in fullscreen mode, you can find them all in the sidebar:
When using fullscreen, you are no longer in a “drawer” type window, but on a dedicated page. The same way as you would be on a regular topic. So the close button is indeed gone.
To switch back to forum mode, you can use the icon in the header:
This will bring you back to where you were in the forum.