1. known for eating...Lingnan,这里的known是引导的状语作插入语吗？

分析：这里的 known for eating the flower buds of popular fruits in South China's Lingnan为 known 引导的过去分词短语作定语（非限制性），修饰前面的名词短语（a stink bug)，相当于一个非限制性定语从句：which is known for eating the flower buds of popular fruits in South China's Lingnan.

2. a province long known for its delicious Cantonese fare 中的known是做状语还是做定语？

分析：a province long known for its delicious Cantonese fare 中的 known...短语也是 known 引导的过去分词短语作定语，修饰前面的名词。（long为副词，修饰过去分词known）。