Another question is, were there whole "ninja villages" that could get paid enough that everyone in the village could sit around or train full time based entirely on the income from assassination jobs?
I remember something about an amount mentioned in the book Shogun but I don't remember what it was or if it was realistic.
(No, I don't watch Naruro. I hate that show.)
The real problem here is that there is no real historical evidence for the existence of ninja as a distinct group. And the problem is exasperated by the fact that you can find plenty of "historical books" by people like Stephen Turnbull that purport to be real histories of the ninja, as distinct from the literary ninja. These books rely on an uncritical reading of the sources. And, thankfully, Turnbull himself has finally made amends for his part in bad ninja history promotion by publishing a paper debunking the ninja, and explaining how he misread the sources.
“The Ninja: An Invented Tradition?”, The Journal Of Global Initiatives: Policy, Pedagogy, Perspective (Volume 9, Number 1: Interdisciplinary Reflections On Japan, 2014).
It's Digital Commons so anyone can read it.
So, the history as stands is that there were people doing "shinobi" work: scaling castles, lighting fires, stealing stuff, spying, killing etc. but there's no evidence for a body of these people as separate from other warriors, or that the people of Iga and Koga were employed across Japan for their skills as ninja.
There are, however, Edo Period literary traditions that Iga and Koga have these skills, so it's possible that those do reflect at least people's earlier views of people or even a few individuals skilled in that sort of work from those regions.
Now, part of the modern legend of the ninja concerns the Oniwaban (popularly known as the Oniwabanshu, mostly because this is what they are called in the hit manga/anime Rurouni Kenshin.) They are portrayed as the ninja who enlisted under the Tokugawa, and thus continued when other ninja were wiped out (or forcibly retired). There isn't any historical connection between Sengoku shinobi and the Oniwaban, but the Oniwaban was a real hereditary group that handled security at Edo Castle and a certain amount of espionage for the shogun. There's not much about them in English, but you might find this entry from my blog interesting: a list of the Oniwaban families, transcribed from a Japanese historical book by a Japanese history graduate student (at the time, she now has her doctorate), and my addition of notes about the Oniwaban and undercover work as found in an interview with a shogunal retainer / Edo magistrate.
Point of correction, Koku is a measure of volume, traditionally one of rice. It was a measure of domain assessment during the bakufu as well as a standard for other measures to be compared to. It was not a currency. The golden ryo coin was commonly used in Edo and the East, the silver monme was more common in Osaka and the West. That's according to the historian Marius Jansen.