Difference between 'be+infinitive' and 'must' while giving order or instruction

I know that `be + infinitive` is used for order, instruction and plan but some of the example sentences are confusing to me they are:

>1. Nobody is to open the door. (order)

>2. you are to do your homework before you go out.( order)

>3. I'm to go now. ( what's the meaning of this sentence ?)
>4. Mr johns was to speak at the meeting last monday. ( is this sentence about past plan or obligation?)
>5. You are to be on time.( is it order ?)

>6. Am I to believe what they say ?( Is this sentence an obligation?)

I'm confused because it's said that `be + infinitive` is used in giving order but i think the meaning it implies is the same to that of 'must' ? So, how 'be+infini' is different than the meaning of 'must' while giving order or when there is obligation? Could you please provide understandable answer? Thank you in advance.