A. Will for the future

We use will to say what we know or think about the future.
Will here has a neutral meaning. It does not express the idea
that we have already decided to do something or that we are
planning something.

B. Will for instant decisions

We also use will for an instant decision, when we decide on
something or agree to do it more or less at the moment of
speaking.
I’m thirsty. I think I’ll make some tea.
NOT l make some-tea.
You’ve left your computer on. ~ Oh, I’ll go and switch it off.
We must celebrate. I know, we’ll have a party.
I don’t think I’ll do any work tonight. I’m too tired.
We also use it to order things.
I’ll have the ham salad, please.
We also use will in offers and invitations (see Unit 51).
Offer: I’ll peel the potatoes. ~ Oh, thank you.
Invitation: Will you come to lunch? ~ Yes, thank you. I’d
love to. Promise: I’ll pay you back next week.

C. The form of will

The form is will or ‘ll.
The west will have rain tomorrow. You’ll be late if you don’t hurry. Will
you be at home this evening? The world will end in the year 2050. The
negative is will not or won’t.
The cost will not be more than £50. I won’t have time for a meal.

D. Shall

We can use shall for the future, but only in the first person, after I or we.
I will be/I shall be on holiday in August.
We will know/We shall know the results soon.
But NOT Everyone shall know the results-seen.
I will and I shall have the same meaning here, but shall is a little formal. Both I will and I shall can be shortened to I’ll, which is pronounced /ail/.
I’ll be on holiday in August. (= I will OR I shall)
Shall has other meanings. We can use it in offers and suggestions.
Offer: Shall I pack up your shopping for you? ~ Oh, thank you.
Suggestion: Shall we all go out together? ~ Good idea.
We do not use shall in American English.