You are correct. In English, the response mirrors the grammar of the original statement. If someone makes a negative statement, you agree with it with a negative statement. These grammatically negative responses are often accompanied by a 'No'. For example: "That's not right, is it?" Agreement: "No, it isn't" (certain) "No, I don't think so" / "No, I don't think it is" (more tentative) Disagreement: "Yes, it is" or "Yes, I think it is". I realise that it seems strange to learners that we sometimes agree with a 'No' and disagree with a 'Yes', but that is what we do in English. The negativity refers to the grammar of the statement, not the view about whether or not the original statement is correct.

If someone asks “it’s not common, right?” and the reply is “I don’t think so”, does it mean I don’t think it is common? Yes, you're correct. It can sound confusing at first. The trick is to understand what the 'so' represents. Replace "I don't think so' with "I don't think it is common either' and it'll probably be more obvious to you

You're correct