Was it possible for Carthage to keep its naval dominance?
Absolutely. To be honest, the Romans adapted to naval warfare against the Carthaginians in a counter-intuitively effective manner. This could easily have been butterflied, as I will explain below.
If the Carthaginian was stronger/bigger (or if the Romans were never able to create an effective navy), would that mean that Carthage would have had a better chance to win the wars? Would Hamilcar Barca have better supplies and resources to use to fight the Romans?
I don't think that the size of the Carthaginian navy was really the key factor here. After the invention of the corvus, the ratio of Roman:Carthaginian losses were in favour of the Romans. But even if the Romans still invent the corvus, it is possible to hamstring the effectiveness of the Roman navy. IIRC, the Romans utilised Tarentine and other Magna Graecian Greeks to crew their ships. Even with the corvus, a certain level of seamanship is required to maneuver into an effective position to use the weapon. The Romans themselves are unlikely to have this skill in abundance.
Which begs the question of how to deny the Greek seamanship resource to the Romans. Whilst it is unlikely that the Romans would avoid expansion into Magna Graecia, the wars against Pyrrhus of Epirus ended only 15 years before the First Punic War. Having Pyrrhus win the wars with Rome is extremely difficult. Whilst he was tactically brilliant, he didn't have the required strategic position to hold Southern Italy in the long term. Furthermore, as long as Pyrrhus was in Southern Italy, Rome and Carthage would remain allies and the Punic Wars would be butterflied away. A much more effective means of denial would be for the Tarentines and other Magna Graecians to put up a more staunch defense against the Romans or engage in some kind of treachery that leads the Romans to slaughter them wholesale. This would fit in well with the Roman mindset of the time, which was both tenacious and incredibly short-sighted. This would essentially amount to the Romans destroying their own future assets. This would greatly increase the chances of the Carthaginians maintaining dominance of the seas, thereby making victory in Sicily a near-certainty. The Romans would be unable to maintain a large fighting force there, and the Syracusans might put up a decent fight, but they'll fold eventually without Roman reinforcement.
If Carthage eventually grew a large enough navy, would it have been possible for them to blockade Italy and cripple the Romans?
Theoretically, yes. Although the Italian peninsula is obviously resource-intensive to blockade, given it's high coastline:landmass ratio. Then again, blockade of the Adriatic coast would essentially be unnecessary. Blockade of the Tyrrhenian, Ionian and potentially Ligurian seas would vastly increase the value of goods going through Adriatic ports, which would only stimulate Illyrian piracy (which was historically a major problem for the Romans, and a key reason that the Eastern side of the Apennines tended to be less-developed than the Western side. But yes, they would definitely be capable of doing so. In my honest opinion, though, the best strategy would be the one they employ in my
now-defunct TL from a few years back, where they exert dominance over Southern Italy and fund the Samnites as a buffer. We also shouldn't forget that a weak Rome is likely to entice wandering Gauls, which without the strength of the entire peninsula at their disposal, are likely to have unchallenged dominance of the Po Valley and menace Latium.