Answer:
1.The answer here is simple when you see what kind a man Ulysses, that is Odysseus is and what Minerva, that is Athena is the goddess of. Ulysses is a one of the best, if not best, strategists of his time and his guile and wits are legendary and respected. Minerva is a goddess of wisdom and warfare, especially warfare strategy. Ulysses is a human embodiment of the traits that she is the patron of an that is why he is favored by this particular goddess.
2.As I sad before Minerva helps Ulysses because of who he is, his traits, and that would be the reason Homer used Minerva to held Ulysses as he embodies the traits she is the Goddess of, that is Strategy and Wisdom. In chapter XIII she says : "We will say no more, however, about this, for we can both of us deceive upon occasion- you are the most accomplished counsellor and orator among all mankind, while I for diplomacy and subtlety have no equal among the gods." This is in the translation by Samuel Butler.