说( Shuo）or 讲（jiang）。。。
chong wen
'I do not speak Chinese' is written as '我不會說國語' in Chinese characters. In pinyin it is 'wo bu hui shuo guo yu'.
Depends what kind. Chinese school in china would just be called a school, or 学校 (shue shiao). A Chinese school abroad that receives funding from the Chinese government is probably called a...
The Mandarin Chinese verb "to say" is "Shūo", 說 For example: 他說你好 (Tā shūo nǐ hǎo) "He says hello."