On what circumstance do you use 'BE TO DO SOMETHING'? It seems to have a modal meaning. Like 'will', 'ought to', 'should', 'must' and so force. But how do you acknowledge which it exactly refers to?

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It has a few modal meanings, but it is quite old-fashioned and very formal.

It's sometimes similar to "supposed to" or "meant to". It can be used to tell people what to do or to talk about something that has been arranged. For example:

"You are to stay here until I get back" ➡ "I am telling you to stay here until I get back"
"The party is to go ahead on Sunday" ➡ "The party has been arranged to go ahead [take place] on Sunday"
"She was to help him with whatever he needed help with" ➡ "She was meant to/supposed to help him with whatever he needed help with"


It can also be used to talk about what should be done, what would be ideal or a good idea, etc. For example:

"What am I to do with all this food?" ➡ "What should I do with all this food?"
"You are to be rewarded if you do well" ➡ "You should be rewarded if you do well (and we intend to reward you)"


We can use it to talk about things that are going to happen, for example:

"The girl who was to marry him" ➡ "The girl who would marry him in the future"
"She is to receive the grand prize" ➡ "She is going to receive the grand prize"
"What is to become of them?" ➡ "What is going to become of [happen to] them?"


Finally, you can use it to talk about what must happen in order for something else to happen, like a conditional. For example:

"If we are to win this competition, we have to work harder" ➡ "For us to win this competition, we have to work harder"
"They must be taller if they are to play basketball professionally" ➡ "They must be taller in order for them to be able to play basketball professionally"