We stood at the top of the moutain __east of the city ,watching__burning rising sun.

相信你是对第一个空有疑问吧?
__east of the city 这一部分在句中充当状语,
方向词如east,west等充当状语,有两种表达方式:
1.和介词in/on/to等连用,此时east是名词;
2.方向词直接用作状语,你问的句子就是这样,此时方向词是副词;
因此,We stood at the top of the moutain east of the city ,watching a burning rising sun.
也可以写成:We stood at the top of the moutain on/to the east of the city ,watching a burning rising sun.

其中介词的用法也有讲究:
1.in 是某小地方在某大地方的一部分内,如:
Guangdong is in the east of China.
2. on 表示两个地方接壤,如Hunan is on the south of Hubei.
3.to 表两个地方不接壤 ,如:Japan is to the east of China.