*the song; this is a song called "Seishun Amigo" sung by the Johnny's Entertainment pair Kazuya Kamenashi and Tomohisa Yamashita under the name "Shuji to Akira" for a drama they appeared in together called "Nobuta! wo Produce." It's a very popular song (:
*penmanship; this is when the students practice their handwritting (usually done in elementary school, I believe)
*how do you say your name?; Different kanji have different readings (chinese reading, japanese reading, and some have different readings alltogether for names), which is why she asks how to say it
*kanji; kanji was borrowed from the Chinese when a Japanese government official (I think) went over to China and saw what they used and basically was like, "oh, we can make our own, too!" Hiragana and katakana are also derived from kanji. (: Also, kanji is typically taken from traditional chinese, rather than simplified.
*stroke names; these are some of the basic eight fundamentals of calligraphy. http://en.wikipedia.org/wiki/Stroke_%28CJK_character%29
*onegaishimasu; this is to show respect, and in judo is said with a bow before and after sparring matches, when entering and leaving the practice hall, when entering and leaving the mat, at the beginning and end of the club activities, before and after contests, and before and after receiving promotions and/or awards. the closest thing to this is a handshake in the Western culture.
*ton suu ton; she's just making sfx. :D;
*senpai; In Japan (and most Asian countries for that matter..) age plays a big part in the respoect hierarchy. Here is just one more example; younger students refer to their older classmates as "senpai", which means "older classmate." The equivilent for younger students (an older classmate calling a younger one) would be kouhai, though senpai can basially call those younger than them however they want (which is why Kyoko calls Yukari by his first name)