The traditional UK English rule is that "shall" would be used in the first person (i, we) for future constructions and "will" for the second person (you, he, she, it). But this is changing in England and has never really been the case in Scotland, Ireland, the USA and other English speaking countries. Hence when in doubt use "will", except in questions and suggestions (read this) like Shall I shut the door? Where shall we go today? Shall we go for a drink?
Shall is seldom used for orders or requests - Will you buy some bread while you’re at the shops? Will you stop making that noise! (although the forms - Could you buy some bread while you’re at the shops? and Make me a coffee, would you? are more polite).
This is a very common way of expressing "futurity"
Shall/will express "futurity" and is almost always used when the future action depends on external circumstances rather than intention. Thus "going to" is strange in the following: a) If you go with him, he'll give you a new one; b) If you ever go to China, you'll see some queer things there; c) You'll always find a welcome here whenever you call. As a simple affirmative statement of intention, with no external circumstances (time, condition, reason etc) mentioned the shall/will future is rare. Going to is rarely found when other clauses are present.
Note that must has the future form shall or will. Don't use going to in the answers - although it would often be valid.
Note - most of these (except 18 - where it is difficult to have an "intention") sound better with "going to" - Why?
Remember that "going to" usually implies greater intention or certainty - and is more usually used with people.
One activity is continuing at a given future time
Note: "he is going to do" and "he'll be doing" have approximately the same meaning but a different FEELING. Thus in: a) they are going to put on another play (soon) we are told the present intentions of the actors, but b) they'll be putting on another play - it tells us the RESULTS of the intention. Thus there are 3 second person questions:
e.g. You are going to see him tomorrow. a) Will you (please) see him tomorrow, b) Will you be seeing him tomorrow.
Although the main clause is in the FUTURE, the presence of temporal conjunctions like when, until, as soon as, before after, while, is sufficient to indicate futurity and the subordinate clause remains in the PRESENT.
The FUTURE PERFECT tells us that a certain action will be completed by a certain time in the future. The time of completion is not of interest but the action itself is. e.g. I shall have read seven of Shaw's plays by the end of the year. or by the time he comes the play will have begun.
The FUTURE PERFECT CONTINUOUS is not very common: e.g. , by Christmas I shall have been working in this office for ten years.
A FUTURE PERFECT idea is expressed by the PRESENT PERFECT in clauses with time conjunctions: e.g. I'll wait until he has written his next novel.