"shall" and "will" for 18th century readers: interchangeable?

Hi everyone,
I've always wondered what "shall" means to an American. Will Americans always take it as "will"? or "should"?

I have always thought of "shall" as kind of a combination of should and will, which made it mildly obligatory though freewill. Below is a context I got from an online dictionary.

    "Shall has some use in all persons, chiefly in formal writing or speaking, to express determination: I shall return. We shall overcome. Shall also occurs in the language of laws and directives: All visitors shall observe posted regulations. Most educated native users of American English do not follow the textbook rule in making a choice between shall and will."

-----Based on the Random House Unabridged Dictionary, © Random House, Inc. 2006

The only common occurrence of "shall" with "I" and "we" is in questions:     Shall I do it now? The alternative "Will I do it now?", is also possible but in British English tends to be regional rather than general usage.

I remember it's Irish English where "Will I do it now?" is OK.

To make clear the above usage, my teacher then went on to explain that General MacArthur was trying to be emphatic by saying, "I shall return", when he should have used "will" to be emphatic (18th Century style).

That's part of the reason why I couldn't remember the rule!

Which does "shall" in the song "We shall overcome." mean, "simple future" or "one's determination"?
If it's used in MacArthur's sense, it's "one's determination."
If it's used in traditional British English sense, it's "simple future."
But it's American song, created around the turn of the 20th century. It was originally "We will overcome." (see Wikipedia article)
Then, it's altered to the phrasing "We shall overcome."