He【主语】// is seeking【谓语动词】// redress 【宾语】//for what he alleges was an unfair demotion【原因状语】.

【2】for介词短语语法结构分析如下

for 【介词】//what he alleges was an unfair demotion【宾语从句】//

【3】what宾语从句语法结构分析如下

what he alleges was an unfair demotion

以上为嵌入式宾语从句(有人也称作插入语)，what在宾语从句作主语成分，即what引导介词宾语从句同时又在宾语从句作主语成分，was为宾语从句系动词be ，an unfair demotion为宾语从句表语成分。