Once again returning to the sea of clouds, Alka looked at the bubbles below. Lucilia's Dream Bubbles were right next to his own. In the outside world, Lucilia was also leaning against him, the living being closest to him.
This implies that in the Dream Realm, the distance between bubbles likely originates from the distance between dreamers in the Real World.
This was the Dream Realm. The Dream Catcher could only bring Alka into it; it wasn't the Controller of the Dream Realm.
So, I still know nothing about the Dream Realm.
The primary ability of the Dream Catcher was to allow Alka to enter the Dream Realm and wander within it. It also allowed him to freely enter others' dreams.
Thus, it became apparent that under normal circumstances, moving freely within the Dream Realm was completely impossible. Leaving one's own dream to enter another's was even more out of the question.
The Dream Catcher's main ability must be to grant the user some permissions within the Dream Realm.