Her cutting the tree down stands out more for the whole ~parallelism to his mother~ thing, but I don't really have a preference? Haha!
I was thinking they could have a kind of... maybe awkward on her end, but extremely happy on his end friendship? Haru's ridiculously interested in the world, and he has no idea he didn't sprout up in Japan like he was supposed to; he's pretty much new to everything, since the moon's all barren and there aren't any trees there, so the woods would just blow his mind.
I'm not sure what kind of character your girl's going to be, but I'm sure by default she'll be leagues more mature than this moron. :| Like a big sister.