How much of the language is required for you to know in you study of your art.
That depends on the art itself, obviously, however a common terminology is important, and, especially in the case of distinct systems, the very specific terminology can have quite a fair amount of importance, to the point where using it is essential for actually understanding the art itself. But, to put it better, here:
The Budo Bum: On Language and Budo
How about a list of some of them
Again, depends on the art… Kenjutsu and Iai:
TIJ: glossary of Japanese sword
Ninjutsu and related:
Glossary of Dojo Terms | Bujinkan Jishin DojoBujinkan Jishin Dojo
It should be noted, of course, that these lists are not exhaustive, and many terms might be substituted or completely omitted depending on the Ryu-ha itself… for example, there are systems that don't use the term "kata" to refer to their methods, instead using kajo (chapter), seiho (powerful methods), or hoke (family method/transmission method)… or the same strike/fist might be called a Shuto Ken in one system, and a Kiten Ken in another… or the same terminology (Ichimonji) could refer to a range of different things, such as a technique, a posture (not necessarily the same posture as found in other systems with the same term being used), a movement, or anything else.
Is Japanese only spoken or is your native language also spoken in class
Japanese only? Only in Japan.
That said, I've been bringing more and more Japanese into the classes I run (traditionally, we've dominantly used English, with my personal instructor not paying much attention to the Japanese terms)… in part due to the prevalence of online discussion, so that my students aren't lost when they see a term on the net, or should they travel to train anywhere else.