request 作动词时 是及物动词，后面可以跟名词、不定式、sb to do、或者宾语从句。
因此，请求做某事，可以有两种说法：
1. request to do sth. 2. request sth. (这个sth是含有动作意义的名词，一般不用动名词)
你说的句子可译为：
1 飞行员请求降落 The pilot requested to land./ The pilot requested landing. （landing是名词，不是动名词）
2 我请求去上海. I request to go to Shanghai. / I request that I (should) go to Shanghai.
反对某人做某事，be against one's doing sth. /object to one's doing sth.
如，我反对他吸烟。 I'm against his smoking. / I object to his smoking. 一般不说 against him smoking. 或object to him smoking