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Ah, I see! Sorry, I did not even think of checking the answers as well :)

Yes, it should be "за меня". But where did you see "за мной"? There is a blank space which is supposed to be filled by a student.

Well, I think I have to point out what is wrong in the exercises, otherwise the link is not so useful.

Sentence 1 suggests:

Пишите сочинение о мире на пятницу. - No one would ever say "пишите...

Maybe you find the following link useful:
Saying 'for' in Russian

There are also some exercises for the prepositions. But I have to admit some sentences in the exercises do not sound Russian at...

I can understand you :) But I do not think it is only a problem of Russian. I have to communicate with English-speaking customers from the US, and I often feel exactly the same as you do. I know all...

I've just found another funny example to illustrate the difference between "для" and "за":

Imagine the situation. I know, you are short of money, since you have been borrowed money from me...

Some more rules of thumb for you. (In this case "for you" is "для вас", since you are supposed to USE those rules, you NEED them, and you somewhat BENEFIT from them).

If you say "спасибо для ваших...