1. 2 Body Hardening OR Martial Arts Techniques. I read this as 2 Body Hardening OR 2 Martial Art Techniques (Not Both)
It should be taken as two powers in total, in any combination, either both of one, or one of each. Bad editing, likely.
2. 2 Body Hardening AND Martial Arts Techniques. I read this as 2 Body Hardening AND 2 Martial Art Techniqiues (Both for 4 Martial Powers)
Possibly. Generally, most styles only supply two powers at level one, but a few do grant more.
3. 2 Body Hardening AND/OR Martial Art Techniques. I read this 2 Body Hardening OR 2 Martial Art Techniques OR 1 Body Hardening and 1 Martial Art Techniques.
Yeah, that's right. Which is what example #1 is supposed to be.
These are some examples in the book that confuse me somewhat
Jujutsu - 3 Powers from Atemi, or SPecial Katas, and/or Martial Art Techniques (I'm guessing 3 Atemi OR and selecy Any Combination of 3 between Martial Art Techniques and Special Katas)
Yes, Jujutsu grants three powers in total.
Dog Boxing - 2 Powers from Atemi, Body Hardenin AND Martial Art Techniques (Does this form actually gets 6 Powers?)
No, just two powers in total, in whichever combination you choose.
Also curious if there is a system out there that utilizes the "If this is your Primary Martial Art Form, then the following other forms can be learned in a shorter time..." system for the Mystic China styles and how the two books overlap in this sense.
That is an element of N&SS in need of serious attention.
Given how few characters can have two styles (and the Mystic China Open Hand stylist can't take any with weapons elements), you shouldn't run into this too often.