...helps me to edit the article ...

If it were simply an honest request, one would say "Can you edit this article by Friday?" One might also say: "Can you help me by editing this article by Friday?" which would imply that one is expected to do the editing oneself, rather than engaging in a cooperative effort. People often, however, indulge in this sort of passive-aggressive behavior, in which they want you do do something for them, but frame it as though they were simply asking for your cooperation.

Thanks, Setanta.

Where I live, this is the usual way to write a request. In fact, it is a polite request. Because we are non-native, it is accepted as correct.

For example, a school teacher, when asking for help, will tell his pupil, "Please carry the exercise books for me." And the pupil will oblige by carrying all the books himself, not expecting the teacher to carry some of the books. In this way both parties are happy.

Can you help me edit the article by this Friday?

This is perfectly correct and asks if this person is able to complete the task by Friday.

The difference in our usage is that '...help me edit...' does not mean that the requester will take part in the editing. The one editing will do it by himself or herself. The requester will wait for the finished product. A native will expect the requester to help in editing. Therein lies the difference between a native's request and our (non-natives') request.