Shall

Your difficulty with shall is not unusual. The use of shall has shifted over time. In the USA, shall is almost never used in general speech and writing, with very limited exceptions.

In the indicative, its meaning is generally totally the same as the verb will. Historically, it is found in paradigms with will, systematically alternating depending upon person:

I shall
You will
He will
We shall
You will
They will

In question form, as a general question, it can mean the same as should, as in voting on public issues: shall a county charter commission be chosen? As a specific question, shall can be a polite and affected way of saying "would you like to" or "may I:" shall we dance?; shall I take your plate? It is also found in a somewhat affected construction "let's …, shall we?" in which it can be used to solicit feedback on the preceding suggestion.

Because of its use in the King James translation of the Bible, you can find it in some quotes, allusions, and fixed constructions.

Today, in the US, if you hear or see shall — apart from quotes, other past references, and some of the fixed uses mentioned above — it is used to show extreme determination, inevitability, or emphasis: we shall overcome.

A non-native speaker could be perfectly fluent without ever using shall.

Shall is used somewhat more frequently in legalese, to add more force or formality than must or will would.     A few examples from documents I've recently handled:

"Licensee acknowledges that any unauthorized use or disclosure of the Confidential Information shall cause irreparable damage to the Licensor"

"... any notice given shall be addressed to the General Counsel of the Licensor ..."

"This agreement shall be construed according to the laws of the State of ..."

You shouldn't use legalese as an example of how to speak everyday English.   Many words have definitions given not by common use or by  a dictionary, but by legal precedent.   A lawsuit over an agreement between two parties may come down to a disagreement about the meaning of a single word in the agreement.   In settling the case, the court sets a precedent that "In a legal contract, the word means this..."   From then on, anyone following that legal precedent will only use that word in the way the court agrees with.

This post looks like a kind of portrait of shall, circa 2012. Wonder if it will feel the same in year 2212.

The rule in the old days was that "I/we shall" is a statement of fact, as are "you/he/she/it/they will", while "I/we will" is a statement of one's determination and "you/he/she/it/they shall" was a command or at least an emphatic request.

The story goes that an American visiting England fell into a pool and couldn't swim. He cried out "I will drown and nobody shall save me!" so all the Brits figured he was committing suicide and telling them not to come after him. If he'd instead said "I shall drown and nobody will save me", they would have understood he was calling out for help.