Qianlong, Falecius, and Lysandros could all help more than I could, but I will say that Rome and Carthage could NOT coexist - mainly due to Rome. Carthage would be fine with Rome confined to Italy, as long as Rome stayed out of Sicily and those other western Med islands, but Rome wouldn't just stay confined to Italy unless it was destroyed or crushed to a point like the Spartans at Leuctra, where they stayed a power, but nothing to regard too seriously while Carthage took the hegemon status. Oh, and I can say that it'd change our world drastically in a lot in some ways (especially language wise), but maybe not AS much as you'd assume in others.
Carthaginian expansion would primarily be focused around Iberia. If/when that's conquered, I don't think you'd see much more conquests. Numidia is more or less Carthaginian controlled, with much of both aristocracies being mixed and with the Libyans more or less being tributary states to Carthage - what I'm getting at is that there's not a lot of reason to go south. Cyrene might be attractive, but probably wouldn't be, and even if it was, the Greek east is more powerful then Carthage - Hannibal can't conquer Egypt or anything like that, and would have difficulties even pushing the Ptolemies out of Cyrene. Carthage could expand down the west African coast, but there's not a lot there worth settling for - small trading missions for their few resources are more likely then permanant settlements. Britain is also brought up as a possible place for Carthage to expand into, but you do have to remember the rather large distance between north Spain and Lands' End in Britain. Carthage might deem its worth high enough it to try and get a monopoly over Britain's tin though. Depends on the situation I'd imagine.
And any Carthaginian empire wouldn't last nearly as long as Rome's did, unless Carthage made a ton of changes to make itself more like Rome. It wasn't nearly as well built for long term survival as Rome - granted, it made it nearly seven hundred years, from 814-146, but I don't think even with Carthage winning that it's got more then four hundred years, given that the Libyans seemed to mass revolt with every invader and even sometimes without it, and a somewhat shaky government.