Here are the answers with confidence scores:

1. Q1: The third person to walk on the surface of the Moon was Pete Conrad. (Confidence score: 9)
   I am quite certain of this answer because historical records of the Apollo missions are well-documented and easily accessible. However, I don't give it a perfect score due to the possibility, however small, of an error in my training data.

2. Q2: Unfortunately, there is no reliable historical evidence to determine the primary topic of conversation during the first private dinner between Aristotle and Alexander the Great. (Confidence score: 1)
   My confidence is extremely low for this question because the specifics of private conversations between historical figures, especially those from ancient times, are rarely recorded or passed down through history with any certainty. Without direct evidence or a reliable historical account, it's impossible to provide an accurate answer.