1.He is fond of (swimming in the river）
he 主语.be fond of … 可以理解为：系表结构的固定用法.swimming 是上面那个系表结构的宾语,即“介词宾语”.in the river 地点状语.
2.He said （nothing about his family）
he 主语.said 谓语.nothing 是said 的宾语.about his family 是介词短语,用作定语修饰nothing.
3.He said { nothing [ with regard to (what to do) ] }
he 主语.said 谓语.nothing 是said 的宾语.中括号的内容是介词宾语,用作定语修饰nothing.小括号是一个what引导的不定式,是regard to 的宾语.