Akagi obtains her crimson red color from her name, which means "red castle" or quite literally "crimson," among others.
Akagi also appears to bathe in flames/engulfed in flames, possibly alluding to her historical demise, where her deck is burning before she was scuttled by a torpedo.
It could also allude to her Chinese censored name which means "Phoenix". Phoenixes die and are reborn through flames.
Self-introduction - Akagi was originally intended to be a carrier conversion along with Amagi, but after Amagi was damaged beyond feasible repair in the Great Kanto Earthquake, the incomplete Tosa-class battleship Kaga was selected for the role.
Return from mission - This is in reference to the "Five Minutes that Changed History," or the Battle of Midway, in which four carriers were sunk in a short time span, effectively changing the course of the entire war.
Additional Voice Lines (Enterprise) - It was dive bombers from the carrier Enterprise which would deal the fatal blow to Akagi at Midway.
Her skill "Preemptive Victory" refers to her participation as one of the carriers that raided Pearl Harbor. She would gain a victory that would not last long, as she would be sunk not even a year later at the Battle of Midway.
Her skill "First Carrier Division" refers to her being in an aircraft carrier unit with Kaga.