I'm on mobile right now and can't provide any of my sources at the moment, but I would highly recommend looking into Croatia and their SS equivalent, the Ustasê. They were a notorious collaborator with Nazi Germany when it came to the Holocaust.

Be sure to distinguish between eugenics (literally "good birth"; eugenics policy usually focused on sterilizing those considered unfit to breed) and euthanasia (manifested in the Nazi policy concerning "life unworthy of life"). Eugenics was popular throughout the western world from the late 19th century into the late 20th century (sterilization continued in the U.S. through the 70s). Euthanasia (employing "mercy killing" for people with developmental disabilities in institutions), the killing of those in a catatonic state that you mention, was never generally accepted. Hitler justified the euthanasia campaign (the T4 program) by claiming the needs of war (http://en.wikipedia.org/wiki/Action_T4#mediaviewer/File:Aktion_brand.jpg). It was the first prong in the homicidal Nazi campaign for an Aryan-dominated greater Reich.

As far as eugenics policies go, it is more accurate to ask who most influenced the Nazis. The answer is the US, which led the world in eugenics-based law and policy for three decades. The Germans openly copied our system, going so far as to name Charles Davenport to their scientific institute. Sweden also had a robust eugenics program that persisted into the 1960s. The Soviets dabbled in it, but found that eugenics and Lysenko-ism clashed. The British had a small but powerful eugenics movement. The term and the original program were the brainchild of Darwin's cousin Sir Francis Galton. Every country in Europe had its advocates during the first half of the 20th century, although the Germans under the Nazis took it further than anyone else. There isn't much claim for serious eugenics movements in any of the Nazi satellites, or on the Iberian Peninsula or Italy, although there certainly were proponents in all those places.

As for your questions, they targeted all non-aryans, as well as anyone with mental or physical infirmities. A catatonic person would be an easy target, although in practice, of the family could afford the cost of care, the government didn't always take an interest.

Some good sources (I'm limiting this to documentaries) are War on the Weak from Global Research TV, The American Eugenics Program from CNN Reports and Documentaries, and Scientific Racism: The Eugenics of Social Darwinism, (easily found on YouTube.)