While it's questionable whether we can come up with a definitive answer to these questions, here is some evidence that at least some of Jesus' (Hebraic Jews) disciples did not know Greek well.
In his Ecclesiastical History III.39, Eusebius preserves writings of Papias, bishop of Hierapolis (AD c. 60–130), in which Papias reports sayings of “the Elder.” There is an ongoing dialogue between scholars about whether “the Elder” is a reference to the apostle John.
The Elder used to say this also: “Mark, having been the interpreter of Peter, wrote down accurately all that he (Peter) mentioned, whether sayings or doings of Christ, not, however, in order. For he was neither a hearer nor a companion of the Lord; but afterwards, as I said, he accompanied Peter, who adapted his teachings as necessity required, not as though he were making a compilation of the sayings of the Lord. So then Mark made no mistake writing down in this way some things as he [Peter] mentioned them; for he paid attention to this one thing, not to omit anything that he had heard, not to include any false statement among them.” (Eusebius, EH, III.39). Papias also comments about the gospel of Matthew: “Matthew recorded the oracles in the Hebrew (i.e., Aramaic) tongue.” (Eusebius, EH, III.39)
McDowell, J., & McDowell, S. (2017). Evidence that demands a verdict: life-changing truth for a skeptical world. Nashville: Thomas Nelson.
If Peter used an amanuensis not only to write down his letters but also to translate them, that would explain the difference in the Greek between his two letters if he used different translators. Note the Greek between Peter’s two letters differs enough to cause some to question the authorship of 2 Peter.
While Papias doesn’t specifically say that Matthew wrote his gospel in Hebrew/Aramaic, it does seem to indicate that Matthew’s first notes he used for his gospel were Hebrew/Aramaic.
The Greek in John’s gospel and letters is very simple although he had lived away from Judea for some time. John was probably about 18 when he was with Jesus. If John knew Greek at that time, you would think he would have become more fluent in later life.
Josephus's writing gives some insight about the first-century language in Israel:
I have also taken a great deal of pains to obtain the learning of the Greeks, and understand the elements of the Greek language, although I have so long accustomed myself to speak our own tongue, that I cannot pronounce Greek with sufficient exactness: (264) for our nation does not encourage those that learn the languages of many nations, and so adorn their discourses with the smoothness of their periods; because they look upon this sort of accomplishment as common, not only to all sorts of freemen, but to as many of the servants as please to learn them.
Josephus, F., & Whiston, W. (1987). The works of Josephus: complete and unabridged (p. 541). Peabody: Hendrickson.
I have proposed to myself, for the sake of such as live under the government of the Romans, to translate those books into the Greek tongue, which I formerly composed in the language of our country, and sent to the Upper Barbarians; I Joseph, the son of Matthias, by birth a Hebrew, a priest also, and one who at first fought against the Romans myself, and was forced to be present at what was done afterwards, [am the author of this work.]
Ibid., p. 543
This is not a definite answer and doesn’t address the Hellenistic Jews. I would like to see more information related to answering these questions.
Here is Edersheim's answer to the language that Jesus used. Ancient Jewish literature supports his answer.
If Greek was the language of the court and camp, and indeed must have been understood and spoken by most in the land, the language of the people, spoken also by Christ and His Apostles, was a dialect of the ancient Hebrew, the Western or Palestinian Aramaic. It seems strange, that this could ever have been doubted. A Jewish Messiah Who would urge His claim upon Israel in Greek, seems almost a contradiction in terms. We know, that the language of the Temple and the Synagogue was Hebrew, and that the addresses of the Rabbis had to be ‘targumed’ into the vernacular Aramæan—and can we believe that, in a Hebrew service, the Messiah could have risen to address the people in Greek, or that He would have argued with the Pharisees and Scribes in that tongue, especially remembering that its study was actually forbidden by the Rabbis?
Edersheim, A. (1896). The Life and Times of Jesus the Messiah (Vol. 1, pp. 129–130). New York: Longmans, Green, and Co.