Shall' is used to tell that something will or is ought to happen ,or is obliged to happen - for example ,''You shall be banished '' normally we do not use shall for asking permission , in case of asking permission i;e should be in a polite way therefore we normally use 'would' , for example ,'' Would you please banish this girl because she is nuisance." 'Will' is less polite when asking for permission,''Will you banish this girl for the sake of our childrens' security'' at the same time it's more like refering to something that will be done in the future . But we can add 'PLEASE' so that it sounds polite, "Will you banish her please." Hope this makes a difference.