As you already realized, many of these questions are left unanswered in the story. And while I would leave digging up any secondary material that might adress them (if existing) to other answers, I'll rather try to reason why they might have been left open and how this, in my opinion, adds to the story. This might represent largely my own opinion, but I'll try to reason based on the text where possible.
Now first of all, from a rather pragmatic viewpoint, it is "just" a short story and there is only so much room for establishing a detailed rule set for how all this actually works. We're getting glimpses of the overarching universe this is set in, by mention of other cities that underwent this process and the presence of some kind of "Enemy". However, all that is left quite vague, just enough as to support the actual story.
But even apart from mere spatial considerations, the purpose of the story seems more to lay on depicting a crucial moment in this setting, throwing you right into the events. We do get some information about the protagonist, but that is more of a "timeless" nature (male, African American, poor, no parental connections), not so much how he came to be. And as few information we get about his past, as few we also get about his future, because that's not what the story is about. In the same way the epilogue is about passing on the baton to L.A., not about what happened to the protagonist in the meantime. Concentrating too much on any transformation the protagonist went through after these events might distract from the overarching themes of city development and the immediacy of the story.
Furthermore, I think the story also profits much from the largely vague and metaphorical narration it employs. Many of its concepts seem to be left deliberately vague and intangible. If you think about the concept of the "Enemy", we don't really know who or what that is. As much as we get from the story, it is something great and old, down at a deep dark place (an almost Lovecraftian evil with its tentacle-bearing undescribable eternal grandeur). And its way of attacking stays equally vague, there are only some hints that they manifest themselves largely as natural disasters to us, when it talks about New York experiencing earthquakes or the allusion to the "failed" cities of Atlantis and Pompeii.
The fight itself has parts that are quite real, but not noticed as that by everyone else
The ground jolts and people think, Huh, subway’s really shaky today.
On the evening news that night, ten construction sites will report wrecking-ball collapses.
But other parts are much more odd and metaphorical
And when it comes at me I hip-check it with the BQE, backhand it with Inwood Park, drop the South Bronx on it like an elbow.
To drive this lesson home I cut the bitch with LIRR traffic, long vicious honking lines; and to stretch out its pain I salt these wounds with the memory of a bus ride to LaGuardia and back.
And just to add insult to injury? I backhand its ass with Hoboken, raining the drunk rage of ten thousand dudebros down on it like the hammer of God.
As the protagonist himself describes it "It’s real but it’s not." It is clear noone else but him actually experiences this fight as he does. In the same way the Mega Cop incident, while being the most substantially unnatural description throughout the story, is also only really noticed as that by the protagonist himself. The people on the FDR honk and scream at him, but seem to just pass over the Mega Cop without noticing, as if it was just devoured by the very city itself.
Now all this vagueness gives the story a very metaphorical quality. All this could actually happen or have happened in our own reality without us really noticing. And I'd go farther and say that all this has happened in our reality already to these or any other cities. To me it comes down to being a metaphor for nothing else but the moment a city becomes more than just an agglomeration of people or a geographic location with a lot of houses, it becomes something of its own identity.
This is the lesson: Great cities are like any other living things, being born and maturing and wearying and dying in their turn.
Duh, right? Everyone who’s visited a real city feels that, one way or another. All those rural people who hate cities are afraid of something legit; cities really are different. They make a weight on the world, a tear in the fabric of reality, like . . . like black holes, maybe. Yeah. (I go to museums sometimes. They’re cool inside, and Neil deGrasse Tyson is hot.) As more and more people come in and deposit their strangeness and leave and get replaced by others, the tear widens. Eventually it gets so deep that it forms a pocket, connected only by the thinnest thread of . . . something to . . . something. Whatever cities are made of.
And to make the turn back from all those ramblings to your actual question, I think keeping with this metaphorical quality requires a balance between not grounding the concepts talked about in the story with too much of an elaborately established rule set. It's the ideas' vagueness that makes them easily connectable to our own reality and, in my opinion, gives them an idealogical grandeur that might be lost from explaining away the mysteries.
That being said, however, there is one question you ask that I think might be answered to some degree from the text. When you ask if the protagonist will have a normal human lifespan after merging with or embodying the city, I think we could issue an educated guess that he won't. Very early in the story, where Paulo is first described, the protagonist alludes to his age and already suggests that it is much greater than it appears:
But he seems older than he looks—way, way older. There’s only a tinge of gray at his temples, nice and distinguished, but he feels, like, a hundred.
When we set that in relation to the later reveal that he is the embodiment of São Paulo, we can see how that earlier allusion could be more than just a figure of speech and it might very well be that Paulo bears an age larger than his human appearance's.
Though, that again is only a hint. On the other hand, this age of "a hundred" might very well be a less literal allusion to the age and soul of São Paulo before it was genuinely born and before Paulo became its representative. So he might still just be a man of normal human age with an "old soul" underneath.