Personally, I'd recommend a copy of Unarmed Fighting Techniques of the Samurai (Hatsumi) and a good kanji dictionary. But remember that some kanji won't be found in most modern dictionaries, as older forms are used, so it won't be completely simple....
Agreed, although I'd expect instructors in the Genbukan, and ideally the Bujinkan to know as well. However Himura is not in those organisations, and his school teaches the Bujinkan Ryu-ha combined with Aiki arts, so the emphasis may not be there. So I provided a reference for his own study. There are others, but it's a good start.
They can have a range of meanings, depending on context, they can also have alternate pronunciations (onyomi and kunyomi readings, basically the native Japanese sounding, and the way the Japanese thought the Chinese pronounced the same character), but more importantly, as Japanese is made up of a small range of syllables, you need to know the kanji to know what the word actually is. For example, depending on the kanji, "Koryu" can mean "old school", "old dragon", "small dragon", and so on. So which kanji do you use?
Sorry to follow myself, but I thought of a better one: Kata.
The first thing that comes to mind when the word is by itself, particularly in these arts, is "form", or "shape", refering to the training drills/techniques. That is written with the following kanji: 型
Alternatively, it could mean "single", as in Katamune Dori (Single lapel capture, Takagi Yoshin Ryu etc), in which case it's this kanji: 片
Once again, it could refer to "shoulder", as in Kata Guruma (Shoulder Wheel, as found in Judo), and is this kanji: 肩
As you can see, knowing the kanji can be essential if you want to get a real translation of these names. By the way, Bruno, how many are you up to now?