I can't find a single ancient source that names Balbus as Jewish. I also see some scattered modern references to this, as you do, none of them particularly reputable. Cicero delivered an entire speech in support of Balbus, and nowhere does he mention it. Balbus was a wealthy, foreign man who rose to prominence in Rome, so maybe the assumption is that he must have been Jewish.

It's possible. I do not know very much about the ancient Jewish diaspora, but I thought that the major movements of Jewish populations happened late in the 1st century CE, after the destruction of the temple. It's possible there could have been a Jewish enclave at Gades 150-200 years earlier, I suppose. Also, Cicero would not be motivated to mention Balbus as Jewish specifically. Romans did not care about race or ethnicity. Everyone who was not Roman were in the same category, with some vague generalizations (Gauls were greedy, Germans were scary, Egyptians were effeminate, e.g.). I don't even know if, in the 60s BCE, "Jewish" was even a meaningful category for elite Romans.

An expert on Hellenistic/Roman Judaism would probably be able to answer this more effectively, but I don't think there are any of those folks lurking around the subreddit these days.