1. Lord Henry Darnley, the handsome poster boy of Scottish nobility, seemed a much better prospect.

结构剖析：这个是一个简单句。主语是：Lord Henry Darnley，谓语是seemed，表语是：a much better prospect。

在表语中much是副词，修饰形容词比较级better。句中的the handsome poster boy of Scottish nobility是做主语Lord Henry Darnley的同位语，说明其长相和身份。

2. It helped that he too had Tudor blood flowing through his veins.

结构剖析：这个句子中的 flowing through his veins是现在分词短语做后置定语。

3. Too late, Mary discovered she had married a lazy, dissolute drunk, incapable of doing even the minimal things required of a co-sovereign.

结构剖析：这是一个简单句。主语是：Mary，谓语是discover，he had married a lazy, dissolute drunk, incapable of doing even the minimal things required of a co-sovereign是宾语从句。Too late是状语，表示时间。

在宾语从句中含有一个形容词短语incapable of doing even the minimal things required of a co-sovereign后置定语，修饰名词drunk。此外，还有一个过去分词短语required of a co-sovereign做后置定语，修饰名词things。