Does it depend on a situation (formal/informal)?
Is one answer more respectful/submissive/dominant than other?
What about an answer to "Are you [...]?" "Yes, I am" / "Yes, I am [...]" or "Yes"? Which one is correct?
It's really context dependent. It depends on who is asking you, why they are asking you, and what they want to know. If your waiter is asking "Do you take cream?" a simple "Yes" is fine. If you're at a party and someone tries to start a conversation by asking "Do you like the band?" a simple "yes" would be indicating that you don't want to talk to them
As non-native speaker of English I want to understand which response is correct, given a context. Thank you for two examples. "If your waiter is asking "Do you take cream?" a simple "Yes" is fine." What if I will answer "Yes, I do" in that kind of situation? Is it too "formal"/""posh"?
Do you agree that "Yes, I do"/"Yes, I am" is always a safer option?