I feel that the English translation differs dramatically between these two translations: You can finish your essay. and You can end your essay. "You can finish" means, keep going until you're done, but "you can end" means, please stop (politely). Which translation is it? (Am I being too nit-picky?)
I think that makes sense. My opinion based on my experience speaking Portuguese is that able to is not really translatable. to elaborate the word capaz usually i find best used for capable or be able to, to express the ability or capability. the verb poder translates to can well directly as like you said can relates to ability or permission in everyday speech.