Is this the correct use of the continuous tense here or would another version be more appropriate in Portuguese?
In Portuguese it works quite well, but in English the "present perfect (continuous)" works better....
Right. The original English is awkward at best. It would be better to say: "I have been working at the library since January."
For sure your suggestion works better in English =)
The English practice sentence is grammatically incorrect. My suggestion would be that DL replace it with MattCunnin7's suggestion.
The English is grammatically incorrect. If you use "since" then you must use a past tense. "I have worked here since..." or "I have been working here since...".