Does my friend like my fiancee ?

From the outside, it sounds like they are in to each other but are trying to deny it (with you as well as with each other). I would have a serious talk with your fiance and find out if he really is ready to get married right now. As long as he is bantering back and forth with another woman in this way - which is not normal when one is in a serious and committed relationship - I would be worried.