Good Questions to Ask Someone.
I'd suggest taking issue with things that specifically bug you the most. I don't want to advocate manipulation but asking questions concerning Joseph's dishonesty about polygamy to his first wife and his marriage of other men's wives and marriage of a 14 year old may prove more fruitful than just saying wow polygamy is messed up.
While you will be of the right age to date, the Church discourages you from trying to date someone while on your mission trip. Trying to maintain a long-distance relationship with someone at home or attempting to date someone you meet while on mission are both distractions.