Addressing body odor
Defenitely in a personal conversation, but you have to ensure the moment is right. In the long run the limited embarrassment she may feel in that private conversation will outweigh the larger embarrassment in public. Start by creating report, e.g. by asking if that persons day/week has been particularly stressful, how they are doing etc. That also provides them with a means to 'blame the situation' and not feel too embarrassed.
Most importantly, if you don't want the relationship to suffer: be sincere.