1. She explained that she didn't want to see John deified nor for John's songs to be part of cult of gloried martyrdom.

划线部分等于 nor did she want for John's songs to be part of cult of gloried martyrdom.

即want后接不定式复合结构作宾语。

want可以有want sb to do sth结构，即后接复合宾语（宾语+宾补），也可以有want for sb to do sth 结构（不定式复合结构作单宾语）。后者不及前者常用。

2. Nike sales doubled in two years and the advert's theme of empowerment and transcendence with a personal philosophy of everyday life formed the basis of  NIke's branding for the following years.

划线部分分析：

主语：the advert's theme of empowerment and transcendence with a personal philosophy of everyday life 其中of介词短语作定语修饰theme，表示同位关系。with介词短语修饰empowerment and transcendence

谓语动词：formed

宾语： the basis of  NIke's branding for the following years.

百度翻译提供了很好的翻译：

这则广告的主题是赋权与超越，并将个人的日常生活理念融入其中，构成了耐克随后几年的品牌基础。