It's kind of used jokingly, or as an emphatic expression. I agree with James, don't simply use it with anyone. It's not a simple matter of "this is the definition, use it in this context". You still need a sense of when it is appropriate to use expressions like this. The same goes for most idioms and slang. Listen for it first. But for an example sentence, "I won't eat fatty foods anymore, no siree!" 'No siree' in this context means "no, not at all (sir)!"

Hmm, technically yes, but no. If you say to your teacher or an unknown man "yes sirree", you are likely to cause some confusion or offence. He may think you are poking fun at him or trying to belittle him. Best to stay away from such expressions!