Many though John the Baptist was the Messiah. He came from the right family and walked and talked the part. The Greeks in particular thought this. They believed that whoever comes first is pre-emanate - those who follow are followers. This is why the Gospel of John spends so much time (in Chapter 1) making the point that Jesus was before John the Baptizer, not after.
Correct. This is what the very thing the Pharisees, Sadducees, and Scribes asked John. His response?
Now this is the testimony of John, when the Jews sent priests and Levites from Jerusalem to ask him
“Who are you?”
He confessed, and did not deny, but confessed,
“I am not the Christ.”
And they asked him,
“What then? Are you Elijah?”
He said,
“I am not.”
“Are you the Prophet?”
And he answered,
“No.”