Are the classes fully in Japanese or in English? Is it a program for kids who don't know an inch of Japanese?

The classes are fully in Japanese. However, there are some small notes to be made. While the classes are all in Japanese, there is an English support service offered by the KCP. Additionally, you can always rely on your English speaking classmates outside of class as well, but hopefully you can soon converse in Japanese with them.

As for the question regarding if this is for someone who doesn't know an inch of Japanese, my answer would be maybe. Personally, I would recommend against it, at least not without getting your feet wet. If I remember correctly, the KCP recommends understanding at the very least the Hiragana and Katakana character sets, as well as being used to some of the grammar and vocabulary. You could go without any knowledge of Japanese, but I feel your experience would suffer because of it.

All class instruction is in Japanese, but supplementary instruction may take place partly in English if needed.