Note:
(a) "Its population of 130,000 belongs to Taiwan, but its island motherland is 120 miles away, and the steel and glass towers crowding mainland China's city of Xiamen beckon to residents of a largely rural island."
The "motherland" alludes to Taiwan. The "120 miles" gives a sense of 天高皇帝远 (while Xiamen beckons).
(b)
(i) "Kinmen Deputy Magistrate Wu Cheng Dian" 金门副县长 吴成典 (新党), appointed by the magistrate. See next.
(ii) 金门县长 陈福海 (December 2014 - ; formerly 亲民党, 击败寻求连任的国民党籍县长李沃士, 成为金门首位无党籍县长)
Remember that December 2014 local election that shocked KMT and started the downhill slide of that party?
(c) "the island's biggest town, Jincheng 金城鎮 * * * Across the [Kinmen] island in the ancient village of Shanwai 金湖鎮山外里"
(i) "biggest" -- not by area but by population.
(ii) 金门县 https://zh.wikipedia.org/zh-cn/金門縣
(section 3 行政区划)