The great things about bitizens is that they never seem to need to sleep. Thankfully you don't have to manage your bitizens personal concerns in this game, as the focus is the tower. Your bitizens will work 24/7 without any loss of productivity, so long as you can keep your shops stocked. So, yes, shops should be open at all times.
If you see them complaining in the Bitbook, I think that's just the developers way of adding some personality into the game. :) The only way to make a bitizen happy in the game is to employ them in their dream job. Failing that, until their dream job opens in your tower, best practice is to match them with the area that they are highest in according to their profile. They will at least remain content until such time as their dream job opens and you reassign them. So long as you can match them with a job of interest level 5 or greater, they will be content. Anything less than 5 and they will be unhappy in their job.