一个很难的英语句子结构的分析---高手进

一个很难的英语句子结构的分析---高手进
After they were inside the temple,they drank their water and ate their moon-cakes-delicious homemade ones,full of dried fruit and nuts.
1、主要指出,full of dried fruit and nuts 这是短语还是句子,做什么句子成分?
2、还有,full of dried fruit and nuts 是不是省略了be,完整的应该是 be full of dried fruit and nuts