Quote 1
(Athene, disguised as the little girl:) ‘So she was held high in the heart and still she is so, by her beloved children, by Alkinoös himself, and by the people, who look toward her as to a god when they see her, and speak in salutation as she walks about in her city. For there is no good intelligence that she herself lacks. She dissolves quarrels, even among men, when she favors them.’ (7.69-74)
Queen Arete is so loved by her husband that she practically has as much ruling power as he does; her favor, not the king’s, must be won by a guest for them to stay in the kingdom, and she settles legal matters with the same authority as her husband.
(Athene:) 'Hear us, Poseidon, who circle the earth, and do not begrudge us the accomplishment of all these actions for which we pray you. First of all to Nestor and to his sons grant glory, and then on all the rest of the Pylians besides confer gracious recompense in return for this grand hecatomb, and yet again grant that Telemachos and I go back with that business done for which we came this way in our black ship.' (3.55-61)
Weird. It's not just the humans who pray to the gods; gods also pray to other gods. Apparently there's a pretty strict hierarchy on Mount Olympus… but being Zeus' daughter does give you some perks.
Quote 3
(Athene:) 'It is true that the young men with their black ship are lying in wait for him to kill him before he reaches his country; but I think this will not happen, but that sooner the earth will cover some one of those suitors, who now are eating away your substance.' (13.425-428)
Athene's "I think" is more like, "I'll make sure." She is the goddess of justice, after all. If she says that something is right, it's right.