The insects in your photos do appear to be aphids. Mature adult aphids have wings and can fly. We sometimes see them arrive suddenly because they are blown up from southern states with weather systems. Often these new arrivals will just die because the plant they land on is not a viable food source. On the other hand, of the plant is suitable, they will settle down and start to feed. This can result in an infestation because the adults can give birth to immature aphids, increasing the potential for damage to your plants. Insecticidal soaps that are labelled for use in organic production, are a good option for aphid management. Spraying them off with the hose is also a good option, it just needs to be kept up until the aphids no longer return to the plants. 
The other symptom that you are reporting, corn stalks falling over easily, is not caused by the aphids. There can be several reasons for corn to fall over like that. Insects feeding on the roots or within the stem at the base, can cause the stalk fall over or collapse. I am including a couple of articles below that have more information about some of the insects that can cause this kind of damage. The articles will tell you how to look for the insects and/or signs of their presence. 

Information on corn rootworm from Purdue Extension: https://ag.purdue.edu/department/entm/extension/field-crops-ipm/corn/corn-rootworms.html
Information on European corn borer: https://ag.purdue.edu/department/entm/extension/field-crops-ipm/corn/european-corn-borers.html