I finished the work, as my teacher told me to.

1) as my teacher told me to 的完整句型是 as my teacher told me to do 吗？既然省略了do可否也一并省略to变为 as my teacher told me 这样正确吗？

【答】as my teacher told me to是方式状语从句，意为：“像老师告诉我的那样；按照老师告诉我的那样”。你的句子是省略说法，如果加了do，就应该说do it，因为do 需要有宾语。补充完整为：

I finished the work, as my teacher told me to do it.

此外，能否一并省略to 的问题，我的看法是：在书面语中最好不要省略，在口语中则完全可以：

I finished the work as my teacher told me.

2) 其次，句中不加逗号可以吗？变为I finished the work as my teacher told me to.

【答】是的，可以不加逗号。一般而言，从句和主句之间加逗号，是为了表示停顿，逗号可以不要：I finished the work as my teacher told me to.

又如，以下表达都对：

He can’t attend the meeting because he is ill.

He can’t attend the meeting, because he is ill.

Because he is ill he can’t attend the meeting.

Because he is ill, he can’t attend the meeting.

3) 再者，句子可否改为:  "I finished the work in the way that my teacher told me" ?

【答】把连词as 改为in the way，句子意思没变。不过，这时的that my teacher told me 是定语从句。其实，in the way 中的in 还可省略，直接用the way 作为连词代替as 即可，这时that 也一并省略：I finished the work the way my teacher told me.