Parag,
In the dojos I've trained in, the first good one charged $45.00 per month from 1994-1996 when typical martial arts dojos were at least $65.00 per month. We also could go to 6 classes per week. They did have to close down though, so maybe their fees were too low. My second instructor had no dojo and taught in the park or at his friend's excercise center and he charged $35.00 per month, but only had 3 classes per week and for the last two years of operation I was doing most of the teaching. The guy who currently leads our group just earned his black belt and charges $25.00 per month. IIRC they guy near you is a high level black belt. The costs usually depend on the experience of the instructor and whether he has his own dojo or not. Another factor is that he is teaching private lessons, which are usually expensive in any art. Those costs are low for private lessons, IMO. My first instructor charged $50.00/ hr.
On those directory pages there are other instructors listed in New York who may have actual dojos if that is what you are interested in.
Historically, if you were born into a ninja clan you really had no choice whether you trained or not. Your training would usually start with your father and later on you'd train with your local instructor. The part about doing chores is typical for many martial arts back then.
By sixth sense in ninjutsu, from my understanding and ability, is to not only detect when someone is sneaking up on you but more importantly detecting attacks before they happen. If someone is attacking me brom behind, I don't only know that they are attacking but I usually feel where they will attack and sometimes even what type. For example, I can tell the difference between a strike to the back of my head and a choke before someone does it. Now, this is in the dojo. In the real world I might have something on my mind which will distract me a bit so I might not be as accurate, thought I will usually know that an attack is coming and from what direction.
IIRC, Dux was in the military but just as a typical enlisted man.
Ninpo is my primary or base style. All of what I learn is sort of incorporated into my taijutsu, including my firearms training. I did train in Eskrima for a while and may train in it again if I have time. I also study military type styles from books and videos to add to my training. Regardless of your training, everyone really has his or her own style. My preference is a traditional style but I do keep up on modern developments. In Bruce's case, he wanted to design his ideal style, one that was best for HIM. Others who have gone that route set up different styles.