帮忙解释下一英语的这种用法1. I eagerly answered all the questions I could

帮忙解释下一英语的这种用法
1. I eagerly answered all the questions I could, because I never worried much about making mistakes.
I eagerly answered all the questions I could, never worrying much about making mistakes.
2.When we climbed to the top of the tower, we saw a beautiful sight.
Climbing to the top of the tower, we saw a beautiful sight.
3.He refused to attend the party, because he didn't want to meet John there.
Not wanting to meet John there, he refused to attend the party.

这有三组句子,每组有两句,意思是一样的.
我想知道这里面用的ing形式,是属于什么语法,怎么用的.
谢谢
我并不关心这是什么谓语动词还是别的什么词,
我就想知道怎么用的,在什么情况下使用.
最好能解释的详细一些，谢谢啦