At my hospital, scrubs are only allowed on nights or if you have been assisting in theatre.
None of the hospitals I have worked in have had accommodation. *I think hospital accommodation is becoming an increasingly rare concept these days, so I would not just assume that it will be available, OP (though I suspect you have looked into this and are not just assuming...). *The places I know where accommodation is available, you need to arrange things quite well in advance, so I would encourage you to sort this out soon as possible as shadowing week is not that far away! *
Food shopping wise, if you are in a city, it is more than likely that there will be a store of some description within walking distance. *As has already been mentioned, internet shopping is also an option. *
As for laundry, the hospital accommodation I stayed in as a student had a washer and dryer, however these were quite expensive to use (I think the washing machine cost £4 per go, and the dryer was either £1 or £2 per 10 minutes). *Not ideal, but manageable.