Short answers, pulled from the story.
The eye of a tropical cyclone is a deceptively calm zone often just 30 to 50 kilometers wide where the sky clears and the wind dies down. This area features sinking air that suppresses cloud formation and creates a clear window to the ocean below despite churning waves.
Tropical cyclones derive their energy from the evaporation of water from the ocean surface which requires sea surface temperatures of at least 26.5 degrees Celsius to initiate and sustain the storm. This heat energy acts as an accelerator that draws in air from a large area and concentrates water content into precipitation over a much smaller area.
The credit for the first usage of personal names for tropical cyclones generally goes to the Queensland Government Meteorologist Clement Wragge who named systems between 1887 and 1907. The naming of tropical cyclones dates back to the late 1800s and early 1900s to provide positive identification of severe weather systems in a form readily understood by the public.
Names of significant tropical cyclones in the North Atlantic Ocean, Pacific Ocean, and Australian region are retired from the naming lists and replaced with another name. This practice helps reduce confusion about what storm is being described when systems last a week or longer or when more than one storm occurs in the same basin.
Between 1979 and 2017 there was a global increase in the proportion of tropical cyclones of Category 3 and higher on the Saffir-Simpson scale with the trend being most clear in the North Atlantic and in the Southern Indian Ocean. A 2019 study indicates that climate change has been driving the observed trend of rapid intensification of tropical cyclones in the Atlantic basin.
When a tropical cyclone passes over the ocean it causes the upper layers of the ocean to cool substantially through a process known as upwelling. This cooling is primarily caused by wind-driven mixing of cold water from deeper in the ocean with the warm surface waters creating a negative feedback process that can inhibit further development or lead to weakening.