Short answers, pulled from the story.
The original Final Fantasy was released in 1987 and was created by Hironobu Sakaguchi. Sakaguchi intended this title to be his final game before leaving the video game industry entirely.
Akitoshi Kawazu designed the battle system for the first Final Fantasy game. He implemented enemy-specific weaknesses and weapon abilities that set a new standard for the genre.
Following Kenji Terada's departure, Takashi Tokita wrote the scenario for Final Fantasy IV and Kazushige Nojima wrote the scenario for Final Fantasy VIII in 1999. Other writers include Masato Kato for Final Fantasy XI and Yaeko Sato for Final Fantasy XIV.
Magical crystals are a recurring element introduced by game designer Koichi Ishii that represents the Japanese classical elements and keeps the world in balance. Control over these crystals forms the core narrative of many entries including Final Fantasy III, IV, V, VI, VII, and IX.
Tetsuya Nomura took over as the main character designer for Final Fantasy VII from 1997 onward. His characters often bear names related to the weather or the sky such as Cloud, Squall, Tidus, and Lightning.
The Ivalice Alliance first appeared in Final Fantasy Tactics in 1997 and later hosted Final Fantasy XII and Vagrant Story in 2000. This world spans a single setting across a large time period allowing for deep narrative connections between games.