Regarding correcting/marking homework
There are many ways to say "correcting/marking homework". The most formal name of the action is "批改" of which 批 means commenting the homework and 改 means correcting the homework.
Many words in modern Chinese are constructed in this manner which is a combination of two characters have similar meaning.
With that being said, when casual conversations, people do not say "批改". Instead, there are several single character verbs:
判作业, mark homework.
老师判你的作业了吗？ Have the teacher corrected your homework?
Personally, I prefer using this one, and it's widely used in places like Beijing, as far as I know.
批作业, mark homework.
老师批你的作业了吗？ Have the teacher corrected your homework?
When I was a student, I normally wouldn't use this one, but some teachers does. Personally I don't like using it in this scenario as 批 also has the meaning of criticise, which also used to refer to the action that teacher or parents scolding a child.
改作业, correct homework.
This is more widely used in Taiwan, and maybe some southern areas of China. Personally I don't use it either as it may be mistaken as the action of correcting the mistakes in homework. For example:
I corrected Tom's homework
我 改了 汤姆的 作业
There is no way to know whether 改 means to mark Tom's homework as a teacher or to correct the errors in Tom's homework without context and inference.
Regarding reviewing homework
The dictionary translation of review is 复习 in this settings. But 复习 literally means to study again or to study again to prepare for a test. See the examples bellow.
- When it just means to study again. For this meaning you can also use the word 温习
Teacher: you should review what you learned today after school.
- When it means to prepare for a test
Student A: Have you prepared for the today's test?
Student B: I meant to, but I spend the whole night playing Diablo III last night somehow.
As you may noticed both scenarios don't fit quite well with your example. In your case review means to look or view again where "again" here is not very important as the homework is already finished and corrected. So the sentence could be modified and translated as following:
Today I reviewed the homework my teacher had marked.
= Today I inspected the homework my teacher had marked. | Today I took a look at the homework my teacher had marked.
= 今天我检查了我的老师给判/改/批的作业 | 今天我看了我的老师给我判/改/批的作业