The mission of the Yamato is a very strict parallel to Operation Ten-Go, the final mission of the historical Yamato. Operation Ten-Go, heavily opposed by vice-admiral Itou as wasteful, had the IJN send one of their last battleships, and the mightiest one at that, to Okinawa in a desperate mission, but was sank in sight of her destination by an attack from a ludicrous number of carrier-launched aircrafts commanded by admiral Mitscher, a feared veteran who had inflicted horrible losses on the IJN before then (at Midway Mitscher commanded the Yorktown, whose aircrafts sank the four Japanese fleet carriers present at the battle). The mission of the space battleship Yamato, opposed as wasteful by Yamato' master-at-arms Itou, had the Cosmo Force send their mightiest and second-to-last battleship (the battleship Kirishima was still at Earth) to Iskandar in a desperate mission, and when almost there is confronted by Domel, who has nearly destroyed the Yamato before then, commanding four fleet carriers with a ludicrous number of starfighters. The difference is, that the historical Yamato was sank, but the space battleship survives the aircraft attack and destroys the carriers.
Historical notes: Marc Mitscher commanded the USS HORNET at Midway, not Yorktown which was commanded by Captain Elliot Buckmaster and was the Flagship of Rear Admiral Frank Jack Fletcher. Yorktown received credit for 1 0f 4 Japanese carriers sunk at Midway (the carrier Soryu). Enterprise accounted for the other 3 (the Hiryu was sunk with the assistance of Yorktown aircraft on the Enterprise). Hornet's lackluster performance at Midway underscores that the "Magnificent Mitscher" was not yet the experienced and legendary commander he became. By the time of the Battle of the Philippine Sea in June 1944, Mitscher had the earned his reputation as a combat commander. Ironically, Mitscher's airstrikes on April 7, 1945 denied Yamato a final battle to the death with six US battleships assembled to meet her. It is tragedy that Yamato and 9 out of every 10 men in her crew were lost in a mission that unlike the mission to Iscandar, not only had no chance of success, but whose real purpose was not the salvation of Japan, but for the Imperial Navy to prove to the Army that the navy still had proper honor and fighting spirit. The greatest tragedy that so many young men died for the pride of old men.
Early in 2202 Earth's fleet is mostly composed of old Kongo, Murasame and Isokaze hulls equipped with wave motion technology and turretted shock cannons, even if Earth can already make ships as powerful if not more than the Yamato (indeed, the Andromeda, the first ship of the new "Wave Motion Gun fleet", makes her public debut in the same battle the older ships above are first seen) and produce them at an extremely fast rate thanks to the time fault factory. It's likely the refitted ships were mass produced during the Yamato's voyage to Iskandar using copies of the wave motion core provided by Starsha to defend Earth from a potential new Gamilas attack, and the new "Wave Motion Gun fleet" only started being designed after the Yamato returned with news that Gamilas wasn't destroyed and there was a new powerful enemy coming.
Yuki's situation in the second season after regaining her old memories at the cost of her new ones: She was collateral damage in a terrorist attack, and when she wakes up, it's five years later, in an unfamiliar place, surrounded by people she doesn't know who claim to know her, and she's wearing an engagement ring apparently given to her by someone she's never met. A total freakout would have been perfectly understandable under the circumstances, even more so if one throws in the reveal from the final episode: she's pregnant (if too early along to show any signs), and the father is the total stranger whose ring she woke up wearing, though at least by the time that this is revealed, Yuki has regained all of her memories, including her love for Kodai which led to her pregnancy.
