And his name means Chickpea. :-)

Evidently (since it's the family name) it's because his ancestors farmed chickpeas, but I still like to imagine it as a personal nickname instead.

I heard it was because of his ancestors' warts

The pronunciation of Latin will vary depending on whether you're relying on classical (restored/reconstructed) or ecclesiastical pronunciation. "Cicero" in the former is [ˈkɪkɛroː], whereas in the latter, it is [ˈtʃitʃero] which is close to the English pronunciation. In most European languages, the pronunciation is closer to the latter (e.g., the Polish "Cyceron"), while, e.g., in Greek it is closer to the former (Κικέρων).

And in modern Italian it's the latter.