What happened to my second half cycle of my half wave rectifier?
I think you may have your oscilloscope set to block DC i.e. it is AC coupled to terminals 4 and 5. Try setting your scope input to DC.

As for your 2nd picture, you must be measuring somewhere different to where you believe you are measuring - double check your scope probe connections. Maybe what is visible is a fuzziness on the o-scope trace and this is at odds with your original trace that was clear. Maybe the ground point of your o-scope is disconnected or maybe it isn't a good photograph?