Yes. they are different ways of descibing the same person.
No.
No. John the Baptist did not write any books in the New Testament.
Elizabeth is the mother of John. Salome is the one that had John killed.
No.
No.
No.
No. John the Baptist was never one of the apostles. John the Baptist's head was cut off in Mark chapter 6, early in the time of Christ's ministry. The apostle John was still alive, and later wrote the book of Revelation. He died on the Isle of Patmos, where he had been exiled.
The name St. Elizabeth usually refers to the mother of John the Baptist who is a different person from Elizabeth of Hungary.
John the Baptist.
No, he wasn't. It was his son who ordered the death of the John the Baptist.
About the same.
John the Beloved was a disciple of Jesus. he was never martyred for his faith. John the Baptist foretold the coming of Jesus and later baptized Jesus. He was beheaded just as Jesus was beginning His ministry.