After the Ambassador had gone to investigate, a man called Horst aimed a fire extinguisher at him under the impression that the Ambassador was on fire . In addition to this , there was a hole in the Ambassador's hat.

参考译文:大使去调查后,一个名叫霍斯特把灭火器对准了他,他以为这位大使着火了.除了这件事情之外,在大使帽子上还有一个洞.

After the Ambassador had gone to investigate, a man called Horst aimed a fire extinguisher at him under the impression that the Ambassador was on fire 

句子语法结构分析如下

时间状语从句:After the Ambassador had gone to investigate

主语:a man called Horst 

谓语:aimed 

宾语:a fire extinguisher

状语:at him

状语:under the impression that the Ambassador was on fire

(备注：that 从句可以看作impression同位语，也可以理解为下面一个固定短语）

under the impression that (误)认为;(错)以为(英文解释：If you are under the impression that something is the case, you believe that it is the case, usually when it is not actually the case)

He had apparently been under the impression that a military coup was in progress. 

他显然以为一场军事政变正在酝酿中

under the impression that the Ambassador was on fire 这句话中，under the impression 是“在印象里”，that the Ambassador was on fire 是同位语从句，对the impression 进行解释说明，这对吗？

解答如下：

是的，可以这样理解为the impression同位语.

2.In addition to “除。。。之外”是否和besides表示一种累加关系，意思相同呢？用法是In addition to+名词，用于句首或句中

解答如下：

in addition to 和 beside意思是相同，都是表示增加更多信息内容.