Aww, that's cute (a bit of spoilers)

[EntiteFred]

I don't know how I managed to do it, but I made Nadja and Li hug a couple of time.  They hug right where they are, and you can't move until you click on them, just like when Nadja sleeps.

[Karn]

That's an idle activity, I believe. Automatically happens. I found it during a certain singing puzzle, and it annoyed me because I thought I had solved it when something was happening... But no.

[lukich]

During one singing puzzle, I got patterns that made me change forms, twice...

[icylace]

When they're hugging each other you can sing to move them around as if you were controlling a seahorse.  If you're curious, the Arnassi Armor has no effect here.