Student or Learner
Are there such saying? Am I writing them correctly? what do they mean?
-"Don't mind if I do".
-"Don't mind if you did".
To add to what billmcd was saying, I'd say that "don't mind if do" carries the connotation of the speaker being eagerly accepting of the offer in question, rather than merely being politely accepting. I remember seeing it used this way in cartoons all the time when a character would reply to an offer with an enthused "Don't mind if I do!" and proceed to indulge to the point of rudeness. :)