Nicodemus

What is meant by Nicodemus "being one of them" (John 7:50)?
He is one of "the rulers - i.e., a member of the Sanhedrin, the ruling council of Israel - [and] the Pharisees" (John 7:48).

When did Nicodemus come "to Jesus by night" (John 7:50)?
Early in Jesus' ministry, as recorded in John 3: There was a man of the Pharisees named Nicodemus, a ruler of the Jews. This man came to Jesus by night and said to Him, “Rabbi, we know that You are a teacher come from God, for no one can do these signs that You do unless God is with him” (John 3:1-2).

How did that conversation with Jesus go?
It went over Nicodemus' head: see John 3, born again, how can these things be, bronze snake, and John 3:16 meaning.

What had Nicodemus been up to since that conversation with Jesus?
He undoubtedly mulled over what Jesus taught him, and would have at least kept up with the news about Jesus. It is also possible, if not probable, that Nicodemus had been in at least some of the the crowds that Jesus taught, especially in Jerusalem. And since the crucified body of Jesus was buried by Nicodemus and another member of the Sanhedrin (see Joseph of Arimathea), it is even possible that Nicodemus had been witnessing about Jesus to his friend in the Sanhedrin.

What does Nicodemus do in John 7:51?
He stands up for Jesus by reminding them of the Jewish law that forbids condemning any accused person until they have had a chance to speak for and defend themselves.

Do they appreciate his reminder?
 

Was it true that "no prophet has arisen out of Galilee" (John 7:52)?
No, the prophet Jonah, for example, had arisen out of Galilee.

Based on John 7:50-52, what is the correct answer to the question in John 7:48: "Have any of the rulers or the Pharisees believed in Him?"
Yes, at least one of them - Nicodemus - believed.