I can't directly answer your questions about Ecuador, though I have been there. I did spend a month in Peru visiting remote health care clinics in the Andeas mountains. I don't know if it is true in Ecuador, but in Peru the health providers are not parallel to what we have in the U.S.. Babies were delivered by "Obstetras", who, as far as my Spanish would take me, seemed to have a training level somewhere between a Certified Nurse Midwife and an obstetrician. Before setting my heart on being a midwife there, I would check out if your training would be of use there.
I found that medical services in remote areas of Peru were in many ways superior to the U.S.. Just because it is a "third world" country, I had kind od assumed that our system/training would be superior. I was wrong. The country of Peru serves their people medically to a higher level than we do here, for a small fraction of the cost. The exception is in cancer care, which is not covered by their national health insurance.
One opportunity that I found in Peru is a program called Projecto Peru, which is a language school in Cuzco. They will set you up with a volunteer position is a hospital, orphanage or school in the city. They also help with either a host family or an apartment. I plan to go for a month or two after nursing school
if I can't land a job. I think it would be a great way to check out a country before moving so far away. Hopefully you can find a similar situation in Ecuador. Good Luck!