The skinny one is just for locking the female connector on, so no worries there. The bottom one is where the fuel goes through, the little pin in the middle opens a small check valve in the male end to allow fuel flow, the smaller section pushes the ball check in the female piece back and allows fuel from your line into the male section. The wider stepped area is where the seal sits, the green stuff is corrosion that was likely causing the leak. You could try cleaning it off with 400 grit wet and dry, but the area where the seal sits needs to be clean. Have a look at the female section and see if the seal is in place and not rolled back, as that will cause a leak as well.
Replacing the male one is quite easy, usually just remove the hose, take out a small bolt and put the new one in. Get the OEM ones as they seem to resist the ethanol in the fuels better. Use a little two stroke oil or Vaseline on the seal area to prevent future corrosion and facilitate easier connection.
