Meaning of "be supposed to"

Dear teachers,
Please explain to me “be supposed to”
“She was supposed to know how to behave properly.”

She was supposed to know how to behave properly.”

This sentence means that people said she knew how to behave properly.

What about " supposed to " which means " a duty" ?

Another challenging question!

As you say, ‘to be supposed to’ can also mean to be expected or required, not only by duty, but also by law, morality, custom etc. (to do something). Now, to convey this meaning, I would just say: “She was supposed to behave properly” (it was her duty to act rightly). Still, it can also mean: “People said or took for granted that…”

I used this phrase when I should’ve been somewhere,but I couldn’t make it.
“I’m supposed to be there at this moment.”
Because noone mentioned this, I’m kind of wondering if I might used it wrong.
Did I?

(she was supposed to know=she should have known,but didn’t,
if you think the way I do)

You are right Spencer, because ‘should’ is also used to express duty. “I’m supposed to be there” can mean I should be there (in your context), but also I’m expected to be there, I’m required to be there or even People say/believe/suppose I’m there. The same applies to your second example.

Dear teachers,
Please have look at my writing. I am not sure of the usage of verbs. Please correct for me.
"My daughter has been trying to find a job for months. She left university in June, and since then she has had one or two part-time jobs. She has been working in a cafe for the last two weeks.
She wants to work in publishing. She wrote hundreds of letters of application, and she had a few interviews but no jobs offers yet.

Only the last sentence needs correcting:

The last sentence refers to actions whose time is not mentioned and which are connected with the present: she hasn’t found her publishing job yet and she may continue to write letters and to have interviews.