The first story sounds a lot like "The Golden Man" by Phillip K. Dick. The publication timeframe is good but it does not appear to have been anthologized, only appearing in Dick's own short story collections. I don't recognize the other story at all but maybe someone else will. Here's the covers for the Dick collections. http://www.isfdb.org/cgi-bin/titlecovers.cgi?37578https://www.isfdb.org/cgi-bin/titlecovers.cgi?37578