They traded blows and wrestled for half an hour, and neither would give way.

参考译文：他们互相斗殴并扭打了半小时，谁也不退让。

句子语法结构分析如下:

主语：They（他们）

谓语(1)：trade（互相斗殴）

宾语：blows（殴打）

并列连词:and（并且）(连接2个并列谓语动词）

并列谓语(2):wrestled（扭打）

时间状语：for half an hour（长达半小时）

引导并列句的并列连词:and（而且）（连接2个并列的A/B分句）

主语:neither（2个人当作没有一个，谁也不）

谓语：would give way（让步，退让）

A分句=They traded blows and wrestled for half an hour,

B分句= neither would give way.

(1)trade blows:互相做;对打;对骂

trade vt.互相做;对打;对骂 (英文解释：If two people or groups trade something such as blows, insults, or jokes, they hit each other, insult each other, or tell each other jokes.） 

Children would settle disputes by trading punches or insults in the schoolyard.

儿童会通过在操场上对打或互骂的方式解决争端。

They traded artillery fire with government forces inside the city. 

他们与城内的政府军互相开炮。

(备注：基本意思为“做买卖;做生意;从事贸易trade with sb/sth”“用…进行交换;互相交换trade sth for sth/sb be traded for sth”“相互动词交换，对换(位置或处境)trade places with sb”“使(足球、棒球等职业运动员)转会sb be traded from”)

They had years of experience of trading with the West.

他们有多年与西方贸易往来的经验。

They traded land for goods and money.

他们用土地换取了货物与金钱。

He still claims the arms weren't traded for hostages

他仍然声称军火没有被用来交换人质。

Mike asked George to trade places with him so he could ride with Tod.

迈克要求乔治和他交换位置，让他和托德同坐一辆车。

He was traded from the Giants to the Yankees.

他从巨人队转会到扬基队。

(2)wrestle 摔跤;扭斗

wrestle vi摔跤;扭斗 (英文解释：If you wrestle with someone, you fight them by forcing them into painful positions or throwing them to the ground, rather than by hitting them. Some people wrestle as a sport.） 

They taught me to wrestle.

他们教我摔跤。

The bridesmaids and pageboys squealed and wrestled with each other in the garden. 伴娘和伴童在花园里尖叫着，扭打在一起。

(3)give way撤退；让路；退让；垮掉

The enemy troops had to give way.
敌军不得不撤退。

You must give way when you come to this junction.
你到了这个路口必须让路。

We are not going to give way to blackmail.
我们不会屈服于讹诈。

They traded blows and wrestled for half an hour, and neither would give way.

▲你的理解是对的，基本上翻译出了原意。trade blows 指“你打我同时我也打你”，wrestle 的意思是“摔跤”，所以 trade blows and wrestle 其实就可翻译成“扭打”。

▲另外，give way 的本义是“让路”，这里引申指“让步”“退让”。如：

You have to give way to traffic coming from the right. 你要让右边驶来的车辆先行。

In arguments, I’m always the first to give way. 和别人争论时，我总是最先让步。

▲其实只要将你对句子的理解稍稍精简一下即可：他们（相互）扭打了半个小时，两人都不愿让步。

They traded blows and wrestled for half an hour, and neither would give way.

【译文】他们斗殴并扭打了半个小时，谁也不肯让步。

   【说明】本句中的两个and（并且）都是并列连词：第一个and连接2个并列谓语动词:traded （vt.交换）和 wrestled（vi.扭斗）。blows（n.殴打）是traded的宾语，trade blows的意思是“对打,互相打”。第二个and连接2个并列句：They traded blows 

and wrestled for half an hour和neither would give way.

    第一个分句的for half an hour（长达半小时）是时间状语。

    在第二个分句中，主语 neither 是不定代词，意思是“两者都不”。注意：neither作主语时，谓语动词应该用肯定式，所以，此句的would（愿意）不能改为wouldn't。本句的give way的意思是“让步；退让”。