A clever case of Gameplay and Story Integration combined with Developer's Foresight - Even Caeda and Minerva can use the Aum staff, as only a princess can use it. Caeda and Minerva are indeed princesses, and under normal gameplay wouldn't be able to use the Aum staff... but if they are reclassed to a bishop or sage, they can.
In the original game and Shadow Dragon, when Marth meets up with Elice and begin the invasion of Doluna, Elice mentions to Marth that the Aum Staff, a staff that can revive the dead, rests nearby and that if Marth lost any companions, it would be worthwhile to grab it. Considering that most players reset when any playable character dies, it makes little sense for FE1 Marth to get the staff, unless he's preparing for the fight against Medeus. His motive for doing so becomes a lot clearer in Shadow Dragon where in the prologue, the player must sacrifice one of their units as a decoy to keep Marth and the rest of the party alive, and canonically, it's established as Frey. But no matter how hard one tries, Frey or whoever you sacrificed cannot be resurrected. This is because in New Mystery, it's revealed that Frey was merely wounded and left for dead by the enemy army, and is in fact alive and well, and he joins the party in full ready to kick ass.
In Shadow Dragon's ending, it's stated that Jake and Anna dreamed about visiting far-away continents. Although we don't see Jake per-se, Anna ends up appearing in different continuities in the series as the in-game tutorial person.
Awakening says that all of these Annas are different characters and expies of each other. More exactly, they're from different alternate universes.
Medeus is called the Shadow Dragon at the peak of his power, but he is an Earth Dragon in Shadow Dragon; In Mystery of the Emblem, however, he is a full blown Dark Dragon. While this is a discrepancy between both games, the only bridge being that all Earth Dragons having Dark Breath as their weapon, remember that in cutscene images in the DS remake, Medeus was in his Dark Dragon form, was mentioned in Shadow Dragon that he wasn't fully resurrected yet by Gharnef, and that outside the Dolhr castle walls he is powerless. With all of that, it makes sense he wasn't a Dark Dragon yet during his first resurrection because he was weak, making it fitting he was in his weaker state, that being the Earth Dragon form. When the Mystery of the Emblem events occurred, enough time, energy, and a more suitable location was used to resurrect him fully, making him go into his more powerful Dark Dragon form.
Related to the above brilliance with the Staff of Aum, why doesn't Marth instead use the staff to resurrect his father or his mother? It's not like Marth cares about succession at the moment and reviving his father to rule would allow him some more freedom for the next few years until he dies again.