The walls remain solid.

And if she tries outside again?

Walls are no barrier to her. 

"Magical objects lose power inside the room, and if they're damaged there they lose power permanently," she concludes.

"Are you sure the newspaper and cross were magical, too?"

"Newspaper, yes; cross, no."

"Okay." Pause. "So did we lose the newspaper and the pencil forever, then?"

"Perhaps."

"...okay, this is kinda annoying."

"Mm."

She sighs. "Well, we should. Like. Test stuff about this room, then, I guess?"

"We probably should."

So Kaede grabs her backpack again and gets a notebook and a pen from there, to start writing possible ideas for tests.

Writing doesn't seem to work on this notebook. 

She shakes the pen and sighs and tries scribbling on a different piece of paper with it.

That works!

It's pen and paper, fairly standard as that goes.

Okay good. Now back to the notebook.

The notebook refuses to be marked, apparently.  

Another pen? Or perhaps a mechanical pencil?

Writing seems to have no effect.

Okay, she tries other pages, then.

Nothing doing. 

"Um."

...she tentatively tries ripping a page off.

This notebook is holding onto all of its pages, thank you very much. 

"—I am pretty sure this notebook wasn't magical before," Kaede tells her mom.