The general scholarly consensus is that the Gospel according to Mark was written some time around the year AD 70. Views differ on whether it was written shortly before the fall of Jerusalem in AD 69, or just after in AD 71.
In either case, Mark would be considered crisis literature. It was written during a period of great stress and trauma which culminated in the fall of Jerusalem and the destruction of Jerusalem's Temple. The end of the Temple, the spiritual heart of Judaism, and the psychological heart of every Jew, was catastrophic for the people.
We do not know who "Mark" is, or even that the book that bears his name was written by someone named "Mark." The title was appended some years after it was written. Nowhere in the text itself is the author identified. (The same is true of Matthew and Luke as well. In the fourth gospel, the author is identified only as "the beloved disciple.")
Some have supposed that the "Mark" identified as author of the second gospel is the John Mark mentioned in Acts, but there is no reason to say so other than the similarity of the two names. In the Greco-Roman world, lots of people were named "Mark" or "Marcus." In any case, even if it was John Mark, we know next to nothing about John Mark!
Some have also supposed that Mark was an associate of Peter's, and that Mark's gospel is distilled from lectures given by Peter. The earliest witness to Mark as the author of the gospel that now bears his name comes from the early church father Papias, an early second century bishop, who said, without citing any evidence, that Mark was an associate of Peter's and correctly wrote down what Peter had told him to write, but "not in order of the things said or done by the Lord."
Papias' remarks are known to us only because parts of them were preserved by Ireneus. These comments of Ireneus were later used by Eusebius of Caeserea in his Ecclesiastical History. Papias' views are not considered definitive. (Eusebius refers to Papias as "a man of very limited intelligence.")
It is Ireneus who firmly attached the names of Matthew, Mark, Luke, and John to the gospels which, today, bear their names. Ireneus was the Bishop of Lyon during the middle of the second century, a time when the young church was under considerable stress. Invoking apostolic authority for the gospels, such as making Mark an associate of Peter's, was a way of shoring up the authority of those gospels.
The theory that Mark was a scribe for Peter flounders in a number of ways. Mark and Peter are never directly associated anywhere in the New Testament. In the patristic literature, the supposed connection between Mark and Peter is never directly and incontrovertibly asserted.
The most telling argument, however, is that Peter is portrayed negatively in the Gospel according to Mark. Mark is sharply critical of the disciples through the book, and especially critical of Peter. The disciples never do anything right, and Peter is regularly shown to be the most clueless of the bunch. If Peter was the brains behind Mark's gospel, then Peter must have been the most humble man who ever lived.
In fact, if anything, the theology expressed in Mark's gospel would seem to be more consistent with the views of Paul than those of Peter. As with Paul, Mark's emphasis is clearly on the cross. Still, many notable Pauline themes are absent in Mark, just as Mark's concern with the teachings and ministry of Jesus is absent in Paul.
Who was Mark? We do not know. Was Mark Jewish or gentile? We do not know. Was Mark written in Rome, Syria, or Alexandria? We do not know.
Let us then speculate. My view is that Mark was Jewish. Some commentators say he could not have been Jewish since he didn't understand the geography of Galilee. In 7:31, he speaks of travelling from Tyre north to Sidon in order to get to the Sea of Galilee which was actually southeast of Tyre. Also in 7:31, the decapolis--ten Greek cities--is mentioned. The decapolis was yet further to the east of the Sea of Galilee.
Mark, however, is not interested in giving us a travelogue. He's in the process of showing Jesus travelling widely throughout the gentile regions on the north and east of the Sea of Galilee--Tyre and Sidon to the north, the decapolis to the east. Mark's point is that Jesus thoroughly encountered the gentiles, and his actions in gentile territory prepare the way for their inclusion. This was important to do in preparation for the second feeding story in Mark (8:1-8).
The first feeding story (6:35-44) took place on Jewish territory, and there were 12 baskets of food left over. "Twelve" represents the twelve tribes of Israel. The second feeding story takes place on gentile territory, with 7 baskets left over. Seven is the number of completion and universality. Taken together, the two feeding stories incorporate both Jews and gentiles into the New Community being forged by Jesus. As per usual, the disciples didn't get this. Mark 8:19-21:
19When I broke the five loaves for the five thousand, how many baskets full of broken pieces did you collect?’ They said to him, ‘Twelve.’ 20‘And the seven for the four thousand, how many baskets full of broken pieces did you collect?’ And they said to him, ‘Seven.’ 21Then he said to them, ‘Do you not yet understand?’
My view is that the itinerary Mark mentions in 7:31 is irrelevant to the question of Mark's authorship. He's not writing for National Geographic. He's writing theology in narrative form and uses Jesus' presence throughout the gentile region as a device for joining Jews and gentiles.
Another argument for Mark being a Jew is the poor quality of his Greek. Mark was certainly not dense. Any study of Mark's gospel will quickly dispell that idea. Why then is the Greek of poor quality? Because he was writing in his second language. His first language was the language of the native Jewish population, which was Aramaic.
As to where he was writing, we have no idea. One view is that Mark was most likely written in the region of Galilee or Syria mostly because the region is important all through the book and because, at the end of the book, the disciples are told to go to Galilee. (Compare Luke, where the disciples are told to stay in Jerusalem.) This is not a definitive argument, obviously. Mark could have been writing about Galilee from somewhere else.
Who was Mark? We do not know, except to say that, whoever he was, his gospel, a theology in narrative form, is one of the most innovative, creative, and brilliant texts ever to be written.