The notion that the Carthaginians "probably" reached the Americas is absolutely ludicrous.
Bernardo de Azevedo da Silva Ramos was deluding himself. Here we have the drawing of the "inscriptions":
And here's the actual thing:
...Yeah, those aren't giant carvings in the rock-face. That's a bunch of grooves left by natural erosion. All subsequent studies have confirmed that.
Note also that this mountain, Pedra da Gávea, is in Rio de Janeiro. That's
not where you'd expect a Carthaginian landing. It's South of the Doldrums. A Carthaginian ships would have to be carried by the trade winds, and those would lead to Guyana and maybe Northern Brazil. If the Carthaginians had landed in the America's, we'd find the clearest evidence of it right there.
As for "at least 2800 Phoenician inscriptions" in Brazil-- that's just wholly made up. He only made a collection of
claims about other supposed inscriptions. In other words: a big collection of tall tales, not one of which has subsequently been substantiated in any way.
Meanwhile, the Paraíba Stone was a notorious hoax; a contemporary counterfeit that was later exposed, and was widely ridiculed.
Conversely, the Carthaginian circumnavigation of Africa (although unsubstantiated) may well have happened. We know they traded all over the place, and they did travel North all the way to Britain (for tin) and were recorded as travelling down the West African coast as well.
That's very much the key thing here, however:
along the coast. All ancient mariners were coast-huggers, because they didn't have the navigational instruments that allowed them to accurately determine their position when out of sight of land. This is why all the old maps are horribly distorted. They couldn't even get the shape of their home regions right! This changes when navigational tech develops. Then we see the maps getting way more "in shape", and this
happens to also be the time when trans-atlantic voyages started getting underway.
Ships from the Classical period, of course, were also designed for the Med, not for the ocean. They could perform when close to the coast, but even then, it got risky in truly bad weather. Sailing out into the blue? Forget it. Nobody's doing that.
In summation: the stories about OTL Carthaginian colonisation in the New World are products of hoaxes and delusions, and there are very good reasons for that. It simply wasn't in the cards. As
@Buba notes, a ship or even a flotilla (they didn't really have "trade fleets") blown off course might well get accidentally reach South Anerica. (It would almost certainly be an trade mission along the African coast, blown West in a storm, landing in the regions of the Guyanas, or maybe Northern Brazil.) But due to their ships being very much unsuited to the open ocean, it would be both a one-off event and a one-way trip.
Could such an incident produce a viable community? Well, maybe. If they had some cool stuff to trade on board, these men (it would be exclusively men) might integrate themselves with some coastal people. They almost certainly wouldn't have horses on board, but possibly some livestock? Maybe? Even then, it would be a very small animal population, which may not be viable.
The humans would get absorbed by the native population, although they would bring disease, and that would be a major shock. Afterwards, mixed-race descendants would be better-suited to survive these diseases, so they could potentially thrive. And come the next trans-atlantic contact, they'd be among the least susceptible to European diseases. (After centuries, they'd also be 'virgin soil', but the OTL Native Americans suffered from the genetic bottleneck of their founding population, resulting in an immune system ill-equipped to handle the diseases. The Carthaginians' mixed-race descendants would have a slight genetic advantage.)
As far as tech goes: unless iron is readily available where they land (highly unlikely), the tech becomes "lost technology" soon enough.
