Sprints and Olympics I wear tight compression sports bra, and one piece tri suit over, this has worked very well. No drag, and enough support in the chest area.
HIM, I wore same sports bra as always, and trishorts, then pulled on a cycling jersey to not get burnt on my shoulders and actually changed into an even more light weight shirt to run, that also covered the shoulders. The minute extra spent putting on shirt and changing is worth not being burnt to a crisp. In the olympics I am not in the sun that long so sunblock still works.
Chafing. I sweat profusely and chafe in everything, always, haven't solved that problem, usually don't wear a bra the whole following week cause I am chafed raw.