I'm unable to determine the culprit due to the blurriness of the insects in the photos. The yellow eggs could be lady beetles or another species of beetle. The insect in the 2nd photo is either a beetle larva or pupa. The 3rd photo does not have an insect in it. 

I think it may be a beetle.  The things after the eggs hatch are the larvae? How do I get rid of them eating the moon flower leaves?  Will they eat other plant leaves?

Thanks for the clearer photo. These are 3 lined potato beetle larvae. Though they can feed on leaves, they are rarely present in numbers high enough to cause severe damage. The biggest risk for plant damage is on potatoes or ground cherries.