after having taken off,the plane flew low over the city

after having taken off,the plane flew low over the city
after having taken off,the plane flew low over the city.
1整个句子是个什么句子或句型?
2句中的after having taken off,take为什么用过去分词?我个人乱说哦：）别介意哦 就是用过去分词taken话那having就应该用have了构成一个现在完成时的句子.
3如果having算动名词的话那taken应该是用原形take吧?
备注：要说一下句子是正确的,新概念的,当然,上面问题2和问题3我认为的认为肯定是不对的.
我们进入焦点，一楼朋友说是此句一个现在完成时态，三楼朋友说是过去完成时，我们在讨论一下。