Uh, wha???? The girl is in the first grade. Four months into the first grade. She might own a diary. She probably has a cute little purse, of the Hello Kitty variety. But these are items you note are missing when your teen doesn't come home one night. I'd think those are pretty odd items for a 7 year old to grab. I wonder if they actually exist.
Most kids are just learning to read in Kindergarten and haven't mastered it by 4 months into first grade. (I realize there are exceptions and some bright kids master these things sooner.) Same goes for writing. It's usually pretty primitive at this age, very basic, lots of their worksheets involve coloring and circling the right answer. Add to that, she has a non English speaking parent who sleeps during the day and not a lot of adult supervision, according to neighbors. If she's advanced in those things, I doubt it was from early exposure to lots of reading and writing in the home. She may be very bright, but if she has a diary, I'd venture to guess she mostly scribbles in it and draws pictures, makes lists, plays school with it, etc.
And a purse? Most kids in the first grade see it as a 'play' accessory, not something they'd grab before they run out the door, let alone run away. I get that she might be a bit of a latch-key kid, but why carry a purse, as a 7 year old, on top of a backpack?
So I agree with what other posters have said, this, to me, sounds like mom is trying to make it SOUND like she ran away.
But back to backpack (that may or may not exist, I'm just speculating here.) Did someone say, or was it mentioned in an article, that they go straight to the park after getting off the bus? Where's her backpack? (She's got one. My kids are in this school system, it's pretty much a requirement.) The apartment? The playground? Missing?