英语句子结构!1.Two thousand years ago a rich and powerful country

1.(Two thousand years ago时间状语) ,(a rich and powerful country主语) (cut down谓语) (its trees宾语) (to build warships目的状语), with which to gain itself an empire.
后半句with which to gain itself an empire. 是带疑问词的不定式,作warships的定语

2.(people主语) (want谓语) (wood宾语) (to cook their food with不定式作定语,修饰wood) 不定式作定语和被修饰的词之间有逻辑动宾或介宾关系.即 to cook their food with wood. 如果没有with 那么就和wood连不上.
例如: He is looking for a room to live in. 他正在找一间房子住下.

1、two thousand years ago是状语，主语是a rich and powerful country，谓语是cut down，宾语是its trees，to build warships是宾语补足语；定语从句中的which是指warships，整个从句是对warships的一个详细说明，他们用这些战船开创了一个帝国。
2、这句话正常语序应该是：people want to ...

to cook their food 是不定式做定语来修饰WOOD,用来做饭的木头。
不定式所修饰的名词或代词是不定式动作的地点、工具等,不定式后面须有相应的介词。例如：He is looking for a room to live in.
There is nothing to worry about.
Please give me a knife to cut...

后半句是非限制性定语从句，是warships的定语，在这句话中，which指代warships,梳理一下就是：with warships to gainitself an empire.从整句话来看，就是，this powerful country cut down its trees to build warships and gain itself an empire with these warships.