Well, I've seen both occur in my local church. Generally, it is our pastor and deacon board who administer communion, but we have had a couple of occasions when a visiting pastor (woman) administered the elements. As for baptism, several years ago, we had a young woman being baptized, who specifically requested that her friend who led her to the Lord be the one to baptize her. This young woman by her own testimony, had been into a life of drugs and rebellion and save for the steadfast love & prayers of this one friend who stuck by her, openly admitted she would likely have overdosed and died. She clearly wanted to not only acknowledge Gods' saving grace, but honor her friend in front of God and church family. There wasn't a dry eye in the house and it was a very precious time for all.