"Shall" is most frequently used in my dialect to make offers or to suggest something. If I want to offer someone a cup of tea, I say, "Shall I put the kettle on?" If my (Irish) girlfriend wants to offer someone a cup of tea, she says, "Will I put the kettle on?" I'm now used to this usage, but to begin with it sounded as though she was asking me to place a bet: "Will I put the kettle on? Or won't I? Go on, guess!"
In a conversation in the pub the other day, one of the Irish people present said that she'd read that the difference between "shall" and "will" in English English was exemplified in the difference between accidental drowning and suicide, 'Accidental drowing is "No-one will save me! I shall drown!" Suicide is "No-one shall save me! I will drown!"' Two English and one Welsh person started laughing at this, whilst the four Irish people all just looked baffled.
I can't work out whether "shall" is performing the same function in all three of these examples, or whether they are different usages. In "no-one shall save me! I will drown!" "shall" is a command: the speaker declaring their intent not to be saved. In "no-one will save me! I shall drown!" the speaker is predicting an event that they do not wish to occur, but which is inevitable. In "shall I...?" the speaker is asking a question about a future event that presumably involves some degree of volition - hence why "will I ... ?" sounds so bizarrely passive to me.
Anyone got any clearer rules that covers those three instances?