Hey, I worked in the Everglades for several years and did my Master's thesis on the recent changes caused by human interference on hydrologic regimes, and its effects on vegetation patterning across the entire historic landscape. So I can really only answer some part of your question. I'll leave it up to expand on how exactly humans influenced the shape of the landscape. In a one sentence answer, the Everglades was barely touched at all until the arrival of Julia Tuttle and Henry Flagler (co-founder of Standard Oil) who built a railroad from the North to develop a township in the Miami region to build resorts and hotels, as well as a freeze-proof orange growing region that would have either been in Everglades itself after extensive drainage. I'll talk about the formation of the Everglades and it's changes, then come back to these efforts to alter its natural state.

For most of the last 150M years south Florida (and therefore The Everglades) region was under the ocean, which led to the formation of the limestone (karst) base that is very important to the hydrologic systems throughout the region. Eventually the sea level dropped considerably which exposed south Florida to above land--it was a much larger area than it is today. Then what happened 5-6000 years ago was a rise in sea level that trapped freshwater over what was originally dry land. I won't get into the processes of how saltwater buffers freshwater, but you can read about the science of it here. St. John's River and the Kissimmee River south of that, which flows into Lake Okeechobee in the present time, are considerably older than Lake Okeechobee and the Everglades, but they've had a very unusual hydrologic regime whereby they were periodically flooded but mostly running below, and sometimes above, the karst topography. At the time, Lake Okeechobee and the Everglades were a relatively dry clay/limestone base.

5-6000 years ago the sea level increased considerably, which shrunk the peninsula considerably. The increase in sea level increased the water table enough that freshwater emerged on land on a permanent basis which led to the creation of both Lake Okeechobee and the Everglades itself. At this time both east, south, and west were at higher elevations and were largely covered in dense forest. The Calusa occupied the western side that was much more expansive than the east and south that was occupied by the Tequesta people who had existed in the area for about two thousand years before European contact. As you can see in the image above, they very rarely interacted with the Everglades area itself, remaining mostly on dry land. There are some reports that they did cross certain areas by foot in the drier areas, or boat, but if they did it was quite rare and I'm sure pretty dangerous given the harsh nature of the Everglades (Gleason et al 1984 pg 154). This essentially left the Everglades untouched until Spanish and more particular the English arrived, driving the indigenous people out (interesting the remaining Calusa were exiled to Cuba).

The first efforts to control the flow of water through the Everglades came from the US Army which somewhat successfully drained a few feet off Lake Okeechobee out into the Atlantic Ocean through a series of canals in 1887. This provided a greater disconnect between Lake Okeechobee and the Everglades, although not in close to enough to completely dissociate the two, and, in fact, some 30 years afterwards, Lake Okeechobee was at its original water level.

The plans by Tuttle and Flagler to build a resort town, an "American Riviera", with a planned freeze-free orange industry in the Everglades itself began the amazingly determined Flagler to drain the entire Everglades to provide land for his orange industry. He successfully dredged a massive canal in 1896 that drained into the Atlantic ocean to the east which drained much more water than any of the canals that are there present. However, this barely affected the wider Everglades area at the time. Flagler began building the beginnings of Miami to the east of the Everglades, sandwiched between The Everglades and the Atlantic Ocean which was several feet higher and considerably drier than the Everglades was, and still is.

Florida Governor William S. Jennings successfully petitioned the federal government, who at the time owned the Everglades swamp, to gain ownership of it through the Swamp Land Act of 1850. Upon his term ended, an interesting man named Napoleon Bonaparte Broward won the seat, largely won by campaigning on a pro-drainage the Everglades, and upon gaining the Governorship gained the rights that Jennings received to drain the Everglades. After some time, this was met with a massive amount of criticism--not because of ecological reasons (which were barely understood at the time)-- but because of the massive financial cost of the exercise. Broward made huge efforts to drain the Everglades (with fervent support from Teddy Roosevelt who supplied a lot of federal money for the project), setting up the Everglades Drainage District, largely for orange and sugar plantations as well as property development. However, his efforts ultimately failed during his tenure, and he lost the following election. However, Broward was not about to give up on his efforts and he petitioned for vice president, but was ultimately turned down by the Democratic presidential nominee William Jennings Bryan.

This battle to drain the Everglades continued for several decades, and more and more canals and levies were built control and drain the area. Tamiami Trail which traverses the Everglades from Tampa to Miami, was completed in 1928 and blocked a massive amount of water that originally flowed into what is the current Everglades National Park, and has had a profound influence on the ecology of the area. The efforts by author Marjory Stoneman Douglas to preserve the Everglades had a profound impact on Floridians and the American people as a whole with the release of her influential book The Everglades: River of Grass (1947) which led to the formation of the Everglades National Park. In 2000, congress approved the most expensive restoration project of all time in the Comprehensive Everglades Restoration Plan (CERP) that focuses on restoring the original hydrology and ecology of the Everglades, and most of this has been concentrated on raising Tamiami Trail to allow more water to flow through to the National Park.

I'm happy to talk more about the interaction between changes in hydrology and the vegetation of the Everglades, but I can't speak much more on anything else not said above.

The book:

McVoy, C. W., W. P. Said, J. Obeysekera, J. V. Arman, and T. Dreschel. 2011. Landscapes and Hydrology of the Predrainage Everglades. University Press of Florida

had a profound influence on my Master's degree and is largely what I use for the text above. I, of course, have a plethora of other sources (including the excelling Gleason et al linked above that goes into the socio-environmental aspect more than McVoy does) and I'm happy to share them on request.

I apologise for grammatical errors or places where you are scratching your head...I wrote this in a hurry! Hope this helps.