Yes, "man" is 'one' and in colloquial English 'you' often replaces 'one' in sentences such as the above. The proper translation is 'Should one make the bed every day?', but 'Should you make the bed every day?' should be accepted as long as one realizes that this 'you' does not actually refer to a person you are currently talking to, but acts as 'one'. I hope that made sense.
Times in German without a preposition take the accusative case without being direct objects. This link has some more examples if you're interested (scroll down to "Some rules for adverbial time phrases"): http://www.dartmouth.edu/~german/Grammatik/Zeit/Time.html