Use of Any and Some

Read the conversation below:
Barbara: Is there any milk left?
Katherine: Yes, there is some in the bottle on the table.
Barbara: Would you like some milk?
Katherine: No, thank you. I don't think I'll drink any tonight. Could I have some water, please?
Barbara: Sure. There is some in the fridge.
Barbara: Do you know anybody who comes from China?
Katherine: Yes, I think there is someone who is Chinese in my English class.
Barbara: Great, could you ask him some questions for me?
Katherine: No problem. Is there anything special you want me to ask?
Barbara: No, I don't have anything in particular in mind. Maybe you could ask him some questions about life in China. Is that OK?
Katherine: I would be happy to do that for you.