Unfortunately for you (and everyone with an interest in this area of history), we have no records from the Carthaginian perspective, and have to rely on outside sources. As such, saying much about the life of a Carthaginian soldier would largely be guesswork and estimation, which can be entertaining but is ultimately just speculation. We do, however, have some details about the other things you mention: weapons and armour. At the time of the Punic Wars, Carthage had been saddled with the stereotype it still bears today, which is that they relied entirely on mercenaries for their armed forces- while mercenaries did make up part of Carthaginian armies, their forces also included levies, allied contingents and even (rarely) citizen soldiers. Focusing just on the troops which would have been used in the Punic Wars, however, we have a few details.

Libyans, Iberians and Gauls served mostly as infantry, with the Gauls typically favouring longer swords for slashing and the Spanish preferring shorter swords (the sword that would eventually become the Roman gladius or the curved falcata). Armour and helmets were pretty uncommon among the Spaniards and Gauls. The Libyans that Hannibal took with him when he invaded Italy became the hard core of his army, eventually being equipped with Roman weapons and armour taken from their dead enemies. Prior to that, they would have most likely fought with long spears and round/oval shields, with helmets and some limited armour. All three peoples also used cavalry: Libyan cavalry was of the shock variety, using thrusting spears and controlled charges, while their Spanish and Gallic equivalents were notably less disciplined but potentially powerful. Numidians of this time, many of whom fought for Carthage, fought as skirmishing infantry and superb light cavalry. Their cavalry rode with neither bridle nor saddle and would shower the enemy with javelins before getting the hell out of Dodge, avoiding close combat unless they had overwhelming superiority. Both Numidian infantry and cavalry used a small round shield. Carthage also fielded small contingents of men from the Balaerics, light slingers who used leather slingshots to throw stone or iron balls at the enemy.

If you want to know more, please ask and I'll do my best to answer!

Adrian Goldsworthy, "The Fall of Carthage" (Phoenix, 2006)

Dexter Hoyos, "The Carthaginians" (Routledge, 2010)