はい hai is a polite way of saying "yes" and can be used in almost any situation. ええ ee is a more colloquial but still polite way of saying "yes" and also carries a somewhat feminine connotation. うん un is a colloquial way of saying "yes" and is closer to the English word "yeah".
As a student of Japanese, I would say that ええ 's meaning is entirely dependent on the tone of the speaker. They could be saying it drawn out, which would mean uncertainty (imagine going 'ummmmmmm') a sharp sound could indicate surprise (imagine 'huh!?') or it could just be like 'yup' with a flat tone