For the first question: Not exactly, but kinda sorta.
Florida is possibly best understood as three states in one:
There's North Florida, which is (with the exception of the big college towns) essentially an extension of Georgia and Alabama - the same cultural currents that made the Republican Southern Strategy work in the post-Nixon years in Georgia and Alabama also worked in places like Duval County and Pensacola.
There's Central Florida, which I think slants demographically heavily toward residents originally from the Midwest, especially along the coasts (though I can't source that one). In the mid-20th century, this region had a fairly high median age, and was part of the then-growing "Sun Belt" of retirement communities.
Regardless of where most Central Floridians came from, this region was also the seat of the citrus industry for most of the 20th century, so was fairly similar to agricultural areas elsewhere, barring Disney World and a couple of air bases (related to Cape Canaveral).
And then there’s South Florida, which is a traditionally Democratic stronghold, with a largely urban population in a developed corridor running from West Palm Beach in the north down to South Miami. A sizeable chunk of population had retired there from the Northeast. Through most of the 20th century, the Spanish-speaking population was heavily centered in Miami. Note: this includes Colombians, Venezuelans, Guatemalans, Dominicans, Puerto Ricans... people with very different experiences and backgrounds than Cubans.
The Cuban exile population happened to be relatively sizable, but more importantly well-funded (notable members include the Bacardi family and the Fanjul Brothers, who you’ve probably given money to today – they sell most of the sugar consumed in the United States), and well-organized (the Cuban-American National Foundation was founded in 1981, but grew out of other, less public groups, including some seriously shady CIA operations like Operation Mongoose and Brigade 2506, the actual boots on the ground for the Bay of Pigs Invasion).
So as a group, the Cuban exiles had what amounted to a disproportionately loud voice in American politics, and, thanks to their organization and federal government ties, a fairly significant effect on politics in Miami and Dade County. They didn’t have anything like the numbers to directly affect statewide vote totals as a voting bloc, though the Fanjuls were hip deep in politics (and have a wonderful cameo in the Starr Report) and had money to spare for things like lobbyists and PACs.
You can have some fun with 1980 census data here, if stats are your thing. Note that persons “of Spanish origin” counted as only 8.8 percent of the total state population (though I think these numbers had to have been gathered before the Mariel Boatlift, which was at most 125,000 people and ended in October – compare to Florida’s total population of 9.75 million in 1980, and Dade County's total Cuban-born population of 407,000, and Dade's total "Spanish origin" population of 581,000).
EDIT FOR MORE STATS. I'M LIKE THAT.