It helps to go back to the actual 'original' meaning here, to understand how these phrases work.
Suppose is a verb, and usually means either to think something likely, or to expect/require something - or both at once:
I suppose you want a lift to school?
This is a person indicating that they think it is likely that the other person wants a lift, and that they expect they are going to be asked for it.
I suppose they changed their minds.
This might be said by someone who was planning to meet someone and they didn't turn up. It means that they think it is likely that they changed their minds. If you suppose something in the past, you are assessing the likelihood of unknown past events; if you suppose something in the future, you are assessing what is likely to happen - you are making a prediction.
This plan supposes that the enemy will approach through the hills.
This means that the plan is based on the assumption or expectation - or even pre-condition - that the enemy will come a certain way.
You might relate this to the noun supposition, meaning an underlying assumption. You will come across suppose used in this way in maths and philosophy:
Suppose that the triangle ABC is right-angled at B. This means that...
Now, taking this basic meaning literally, when someone is supposed to do something, it means that it is assumed or predicted that they will do that thing. However, meaning has shifted. For example, to bowdlerise a famous film quote:
You were only supposed to blow the doors off!
That is not about a prediction in any normal sense. It is about what a person was instructed to do.
Of course, supposed has become more like an adjective that requires a prepositional phrase, now, but it all comes down to that verb meaning.
So, your friend's example:
The house is supposed to be bought in the auction.
This is the 'original' meaning of supposed, meaning that someone is assuming or thinking it likely that what will happen in the future is that the house will be bought in the auction. It's awkward phrasing, but it's okay. We'd usually talk about a house being sold in the passive voice, rather than it being bought, at least in British English. We would use bought in the active voice, or sold, depending on whether the subject is the buyer or the seller.
Your examples, however:
I am supposed to go home early today
She was supposed to bring nachos to the party
These use the drifted meaning of what is expected because it had been instructed or promised. You could argue that they are still about expectations/prediction/likelihood, because the fact you have been told to go home early means it is likely that you will go home early. The fact that she said she would bring nachos means it is likely that she will bring nachos. However, this sort of obligation expectation is easy to think of as a separate meaning, and people will still use it in cases of obligation where they don't expect a person to meet their obligation (including, quite often, parents who ask their kids to get home early).