No, Alex Rodriguez's first appearance in a World Series was in 2009. The MVP of the Series was Yankees designated hitter Hideki Matsui.
No. Bill 'Moose' Skowron played in 8 World Series but did not win an MVP award.
Yes he won two MVP's one American League MVP and World Series MVP in 1973
Jermaine Dye was the series MVP
Win an All Star Game MVP and World Series MVP in the same season
Derrick Jeter
Livan Hernandez of the Florida Marlins won the World Series MVP award in 1997. He also won the the NLCS MVP award that year. Willie Stargell, Darrell Porter and Orel Hershiser are the only other players to win the league championship MVP and World Series MVP awards in the same season.
Mike Schmidt, Philadelphia Phillies 1980. Schmidt was a unanimous choice for the NL MVP and won the World Series MVP against the Kansas City Royals. Buster Posey won the 2012 NL MVP award and the World series in 2012. He was not, however, World Series MVP.
Willie Stargell of the Pittsburgh Pirates was the Most Valuable Player of the 1979 National League Championship Series and the 1979 World Series. He also won the 1979 National League MVP Award (shared with Keith Hernandez of the New York Mets). Stargell became the only player to win all three MVP awards in the same year.
Derek Jeter of the New York Yankees won the World Series MVP award in 2000. He also won the All-Star game MVP award that year. He is the only player to win both awards in the same season.
Derek Jeter of the New York Yankees in 2000.
Mickey Mantle was the first switch hitter to win the AL MVP. The year was 1956.
Bob Gibson of the St. Louis Cardinals won the World Series MVP award in 1964. He also won the award in 1967. Sandy Koufax, Reggie Jackson and Gibson are the only players to win the World Series MVP award twice.