1. But there was really only one way to get her throne back, an appeal to her cousin Elizabeth.

结构分析：这个句子是个简单句，其中的to get her throne back是动词不定式做定语修饰名词way。

An appeal to her cousin Elizabeth是名词性短语作同位语，做way的同位语，说明这个方式是什么。

2. She must have supposed her stay would last a month, a year at the most.

结构剖析：这是含有宾语从句的复合句。主句是：She must have supposed，从句是：her stay would last a month, a year at the most。

主句使用了虚拟语气。主句的谓语结构是：must have supposed。这个属于情态动词的虚拟语气的用法，must have done表示对过去了的事情非常肯定的猜测。

3. Had she known the real answer,19 years, she would surely have avoided the passage across the Solway Firth.

结构剖析：这句话是非真实条件虚拟句。主句是she would surely have avoided the passage across the Solway Firth，条件状语从句是：Had she known the real answer, 19 years。

条件状语从句中由于省略了if这个引导词，就必须采用倒装句式，将助动词had提到句首：had she known the real answer。

这个复合句使用了虚拟语气，主语的谓语结构是would have avoided，提炼一下就是would have done这个结构，表示与过去事实相反的情况。（详细分析：玛丽女王不知道横渡Solway海湾到达大不列颠需要19年，如果知道的话，她就不会采用这条路线走，可是事实玛丽女王采用的是这条路线。）

由于主句采用的是过去时态would，那么要注意从句和主句的时态相呼应，由于know the answer这个行为发生于avoided之前，所以条件状语从句使用的是过去完成时had known。