Is it safe to use the sauna for 30 minutes and then nurse a baby?

YES. Souna bath is relaxing. Nursing the baby with a relax mood is gratifying to both mom and baby.
Should be fine! Just as long as the baby isn't in there with you.... ( (well, I just had to say that.)) there is no problem with nursing after a sauna. Give yourself a chance to cool down and drink some fluids first.