很棘手的问题，大家快来帮我啊，救命~！！

Being able to finish my work in advance made me happy.就可以了。
Being able to finish my work in advance是一个短语，不是句子，不可以后面加非限定性定语从句，也就是which开头的那个分句。

都不妥当，可以这么写：

I'm very happy because I finished my work ahead of time.

Being able to finish my work in advance made me happy。 就对了。