The Roman officer's question to Paul, "Do you speak Greek?" calls into question the average Jew's ability to speak Greek.
Note the following answer while not direct supports the idea that Paul spoke Aramaic/Hebrew because it was better understood by the people there.
Here is some New Testament Evidence that Jesus spoke in Aramaic influenced Hebrew:
1) It explains the difference between Luke and Mathew’s wording of the Lord’s Prayer:
In Aramaic, Jesus had available to him the word khoba which means both debts and sins. Greek, like English, expresses these two ideas with separate words. When the Lord’s Prayer was translated into Greek, there was a problem. Matthew chose debts and Luke managed to use both words. Whichever word is chosen for worship in English, the faithful need to remember that they are asking for forgiveness for failing to fulfill what God requires of them (debts) and for their failure to do the right thing when they did act (trespasses).
[Bailey, K. E. (2008). Jesus through Middle Eastern Eyes: Cultural Studies in the Gospels (p. 126). Downers Grove, IL: IVP Academic.]
2) It explains the Aramaic play on words the passage about no servant can serve two masters before the Parable of Lazarus and the Rich Man:
THE PARABLE OF LAZARUS AND THE RICH MAN (Lk 16:19–31) …
A few verses before the parable of Lazarus there is a short poem on God and mammon (Lk 16:9–13). …. This text exhibits a play on words in Aramaic, which was the language Jesus spoke at home. He says:
If you have not been amin [faithful]
in the unrighteous mammon [your material possessions]
the amuna [the truth]
who will ja’min ith kun [entrust to you].
The root amn, which appears in the word amen, is used here four times.
[Bailey, K. E. (2008). Jesus through Middle Eastern Eyes: Cultural Studies in the Gospels (pp. 378–380). Downers Grove, IL: IVP Academic.]
Note: I am not trying to debate, but seeking an answer. Here is a passage that tends to support your answer:
Acts 6:1. The related questions to this passage are:
1) How unfamiliar were the Hellenistic Jews to understanding Aramaic/Hebrew?
2) How able were the Hebraic Jews to understand Greek?
I think we would understand that Paul addressed the Hebraic Jews.
Are there archaeological finds, such as ostraca, that would support an answer to these two questions?
Hellenistic Jews and Hebraic Jews in Acts 6:1