Translation:I come from South America, but live in North America.
Lebe and wohne are both correct in this sentence. "Wohnen" means specifically where you live (reside, lodge, dwell are synonyms.) "Leben" is exactly like the English verb "to live," meaning "to be alive," so it can also be used like: "Ich lebe, mein Herze, zu deinem Ergötzen" "I live, my heart, for your delight" [J. S. Bach, BWV 145]
That's also possible.
It's a bit like how in English you can say "I eat and drink" or "I eat and I drink" -- the subject for both verbs in the two clauses joined with "and" is the same and so the second "I" can be left out if you want.
That said, it would probably be clearer with the second ich in it -- but it's not strictly necessary.
Another possibility is Ich komme aus Südamerika, lebe aber in Nordamerika which would also be a bit better than the current sentence (in my opinion); this uses aber as an adverb rather than as a conjunction.
The ich is (or can be) omitted but the "ghost" of it still fills up the first position of the second clause so that the second clause starts (on the surface) with the verb.