Prediction based on opinion.
I think the Conservatives will win the next election.
A future fact.
The sun will rise at 7am.
Promises / requests / refusal / willingness
I’ll help you with your homework.
Will you give me a hand?
I will give up smoking!
In the same way as the future continuous, but with state verbs
I’ll be at the station when you arrive
‘Shall’ is used mainly in the forms ‘shall I ?’ and ‘shall we?’ in British English, when you want to get someone’s opinion, especially for offers and suggestions.
Shall I open the window? (=do you want me to open the window)
Where shall we go tonight? (=what’s your opinion?)
We use ‘be going to’ + infinitive for:
Future plans made before the moment of speaking.
A: ‘We’ve run out of milk.’
B: ‘I know, I’m going to buy some.’
Prediction based on present evidence.
Look at those boys playing football! They’re going to break the window.