This construction usually implies a request, and your examples are all correct English. But depending on the context and the speaker's tone, it can convey anything from a polite request to an angry order.
Of course, "Will I do something for him?" sounds more like the speaker genuinely doesn't know what he/she will do, or that he/she is asking a rhetorical question not meant to be answered (or whose answer is already known).
The second question isn't a question at all; it's a sarcastic rhetorical question whose answer is already known.
By the way, it sounds more polite to say "Would you" or "Could you" do something. "Will you" can easily sound like an order depending on the context. I might be slightly offended if someone said to me:
Will you close the door? It's freezing in here.
The implication is that I'm too stupid or inconsiderate to close the door despite the cold weather.
But either of these would sound more polite to me:
Would you close the door? It's freezing in here.
Could you close the door? It's freezing in here.
I don't know why, but the subjunctive mood usually sounds "softer" and more polite, probably because it implies a possibility instead of something definite.