I'm a little confused about "pracuji"--isn't the first person singular form of this verb "pracuju"?
One of your suggested answers is "I have worked on it for five months." I don't think this is right, because in Czech the verb is in present, and this translation is definitely in past tense: (I have worked on it and now it is done). I can live with "I have been working ...." because of the peculiarities of the English language on this issue. What about "I am (already) working ..."?
No, the present continuous or simple cannot be used here, at least according to my (albeit limited) knowledge of English. The present perfect is in order here and I don't see a big difference between "I have worked" and "I have been working" in this regard.
I am not a grammarian, but from my native AmE perspective, "I have worked on it" does not definitively indicate that the "working" has come to an end, in that way that "I worked on it" would. I don't see any place for "already" in the English translation, because there is nothing in the original that would suggest it should be there. But if there were a place for "already," it would be used as "I HAVE already been working on it" rather than "I AM already working on it." There's nothing wrong with the phrase "I am already working on it"; it just doesn't belong with the following "for five months" part of the sentence.