'Shall' is a modal verb. Modal verbs (also known as modals) are used to give more information about the main verb. 'Shall' is used to talk about necessities and give offers. For example:

'Must' is a modal verb used to talk about necessities, likely events, and suggestions. Have a look:

We use 'shall' and 'must' to talk about necessities.

Modal verbs are used to create negative sentences and questions.
To create negative sentences, we add 'not' to the modal verb as illustrated below:

Take a look at these examples:

We can create yes/no questions and wh-questions with modal verbs.
Yes/no questions are made by putting the modal verbs at the beginning of the sentence followed by the subject and the main verb. For example:

To create wh-questions, we start by a wh-word such as what, when, where, who, why, and how followed by a modal verb, the subject, and the base form of the main verb. For instance:

We use 'shall' to make formal offers. In this form, we need pronouns 'I' or 'we' to accompany 'shall.' We cannot use 'must' in this context as it will convey a sense of order. For instance:

'Shall' and 'must' are both formal when talking about necessities. However, 'shall' is way more formal than 'must,' and since 'shall' is very uncommon, it may sound pretentious and unnatural. Therefore, in normal contexts, we mainly use 'must.'

'Must' is used with conditional type 1. In this type of conditionals, we are talking about a condition and the results that follow. These conditions have a high chance of occurrence. For instance:

You may hear 'shall' in conditional type 1 statements, but this usage is mainly dedicated to dialects.