There are no demo guidelines. All of these questions depend on what you want to accomplish with it. If the demo is meant to attract future players, and the story is important to the game's appeal, then include it.

First of all, if I'm interpreting your post correctly, you're looking to make a tech demo rather then a game demo. Quoth the Wikipedia:

Quote:
A tech demo (technology demonstration) is a prototype, rough example or an otherwise incomplete version of a product, put together with the primary purpose of showcasing the idea, performance, method or the features of the product. They can be used as demonstrations to the investors, partners, journalists or even to potential customers in order to convince them of the viability of the chosen approach.
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A game demo is usually distinguished from the full game not by being unfinished or untested, but by deliberately including only a portion of the full game's content (released to advertise the game and prove its quality to prospective players).

If this is the case then the rules and goals change drastically. A tech demo is all about the core of the game, whether it's the story or the gameplay or the graphics. Take the most distinguishing and important elements of your design and work on creating a demo that showcases them in the best way possible. Make sure that your demo and design document align here, and change either one as necessary to get a demo you're pleased with.

Should you disable menu options? What menu? It's usually beneficial to strip the demo down to the bare bones and only include the core elements of the game. Potential partners are unlikely to be impressed by having to click through a menu with only one option, and you're unlikely to need a large variety of configurable options in a demo, a couple of command line parameters should suffice.

Whether to include backstory, and how much, is dependent on how important the story is to the game. If you're making a Final Fantasy game you should probably use the demo to introduce important characters and hook players on the story, whereas if you're making another Half Life you can just forget about the story and drop the player in demonstration level that shows off the best gameplay elements.

As for the length of the demo, use your best judgment but remember that much of the work that goes into the tech demo may be changed or thrown away entirely. Don't break your back before development has even started--one level or area is probably sufficient--but do make sure to include all of the core elements from your design document.