Which team did the "Big Red Machine" of the 1970s represent?

What was the name of the Astros' domed home from 1965 to 1999, once called the "Eighth Wonder of the World"? What was the name of the Mariners' domed stadium from 1977 to 1999? What was the name of the Twins' domed home from 1982 to 2009? What was Rogers Centre in Toronto originally called when it opened in 1989 with the first retractable roof? Which Big Red Machine catcher is often called the greatest catcher ever? Which Big Red Machine second baseman won back-to-back NL MVPs in 1975 and 1976? Which manager led the Big Red Machine? Which manager won World Series titles in both leagues, with the Reds and the Tigers?