This reply assumes you don't live on Bermuda.

I don't think you can rely on anything, and indeed the best thing to do is to leave it until BA have got themselves sorted. I would just purchase anything you need, keep and photo the receipts, and just bill them for it. I've only ever heard of one situation where BA were reluctant to pay for something and that was a case where the claim seemed somewhat exaggerated. Otherwise BA pay up quickly and without hassle. Note that BA won't pay for laundry costs, for some strange reason, so you may as well buy replacement clothing. And check your travel insurance too.

If you are in any doubt about this, just search for delayed baggage or missing baggage and you will see anecdote after anecdote about this, the key message being that there is very little you can do in the current situation other than to buy replacement items. In your position I would be buying 2 days worth of clothing.