I've read that it has no local storage. Does this mean no local files whatsoever, or does it just mean that there will be a limited amount of local storage that will be synced to the web somewhere? In that case, where would they be stored and with what limits.
It means that it will have no user accessible local storage, such as what Windows Phone and various Apple product offer.
It needs a place to keep its own files and cache/stream data from the internet, however I suppose it most likely will just have a low ( < 25GB ) SSD drive.
The last part about the size is mainly speculation on my part, the fact is, it is designed to keep all your data in the "cloud" and simply sync down what you need, when you need it. As long as people have fast internet connections, I don't see the need for much more than the minimum that the OS itself needs.
As for filing system, it will be either GFS (Google Filing System), shared/synced with your other Google based devices or more likely EXT4 or some other sort of Linux based filing system.