As for her being the last Lorekeeper, that is true at the time she mentions it. When she said it, she was indeed the last Lorekeeper of the Draconids, but that does not in turn mean she is the last Lorekeeper that would ever be, just that she was the latest one. Throughout the Delta Episode, particularly as seen in the Sky Pillar (with the exposition and the back story), Zinnia groomed the PC to take over the role. The PC succeeding with Rayquaza where she had failed and your final battle with her was the last test of worthiness to the title. She was never supposed to be the Lorekeeper, the old lady at the Dragon Falls said so much, but when the chosen one died, there where no one else to take up the mantle, and she strained from the responsibility (and loss).
And in regards to the PC being a Draconid, it was fairly heavily hinted at from the get go that the PC was special in more ways than just being the designated protagonist of the game. Logically, a tribe/ethnic group such as the Draconids would eventually split into smaller groups as it grew, and some of those groups would, again, logically, travel to and settle in other regions. Heck, they did so within Hoenn, one group stayed near Meteor Falls, while another moved to and settled Sootopolis (handily explaining why Wallace knows as much as he does, as well as explaining why he is part of the group that guards the Cave of Origins). It is far from illogical that such a group would move to and settle in Jotho, which incidentally is where the Protagonist is from. The PC's bond with pokemon goes far beyond most other characters in the game, including ones that bond heavily with their pokes. Only a handful of other characters in ORAS reach the same level, one is the alternate protagonist (obviously), one is Wally, and the rest are either a confirmed Draconid (Zinnia), or suspected as such (Wallace, Lisia, Steven). And then of course, there is the fact that the Lati@s chose to become part of your team. One thing is a coincidence, many coincidences stop being such.