Re: the first day's contest
A big dog toy means a big toy that would be used by a dog.
A big dog's toy means a toy that belongs to a dog that you know is big.I would never interpret this to mean the first.
We still have to employ common sense.
Does anyone actually think there is a school for good girls and a school for naughty girls? Okay, sure, a lot of teenage boys might wish there was a school for naughty girls, and they could break into the grounds, but let's be realistic.
There are very, VERY few times when you're left in genuine confusion about what is modifying what. If you're not sure, then the writer did a bad job. If you're the writer, the use of a hyphen or a recasting of the sentence will save your readers from trying to figure out what you meant.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.