Shouldn't the translation be: "She just finished reading the paper." or "She just read the paper." ?
No. It's simple past we're dealing with and "she finished" is the normal way to say what's been put forward here. There is no indication of duration or specific time points. We don't know if she "just" finished reading it. Could've been a few seconds ago, could've been last week, all we know is that her action of reading it concluded some time in the past.
quote: "In Portuguese there are some verbs that get their meaning adjusted when adding a de to it. ACABAR means to end, to finish. When you place a de after the verb, it takes on the meaning of to have just."
Não, ex: "Minhas aulas vão acabar em dezembro." - "My classes will end in December."
Acabei de ler o jornal = I've just read the newspaper/I've finished reading the newspaper.
Acabei a caminhada = I've finished walking.
How would you say "she stopped reading the newspaper"? I.e. she terminated her subscription or stopped reading it regularly for other reasons.
Daí tem que ser "She has just (finished reading/read) the newspaper".