Girls und Panzer/Headscratchers

Why did the Selection University Team accept the match with Oarai in Der Film?

 * Someone needs to give the University Team in Der Film a good long What the Hell Hero Speech ... they're the heroes of their own story, but playing with the ridiculous set of advantages they do — thirty-to-eight odds and much more advanced equipment, in an annihilation battle — isn't remotely sporting behavior. Basically, they've agreed to be hit-women on behalf of a Obstructive Bureaucrat from MEXT. It seems none of them thought to complain, "Wait a minute! These odds make it look as if we can't win fair and square!" and refuse to go along with the official's scheme. So much for the claim that tankery will make them better women.
 * The head of the team, Chiyo Shimada, is much like Shiho Nishizumi, a powerful matriarch of a major tankery style with a drive to win above all else. She is using this match as an opportunity to put one over Shiho -- she calls her daughter Alice (commander of the University team, and similar in many ways to Maho and Miho) ahead of the match and specifically instructs her to "destroy the name of the Nishizumi style".  The rest of the University team may be similar in character to Kuromorimine (prior to Oarai's victory), composed of enough students who believe in victory as the ultimate goal (as Erika Itsumi did -- Azumi, Mayumi, and Rumi behave this way) or who pretend to out of fear (as many other Kuromorimine commanders did) to keep the rest in line.  As for tankery making people better women (or not)...yeah, the more we see of the tankery world, the more it seems that girls turn out okay in spite of it rather than because of it.

Why was Yukari unable to make friends until now?

 * Tankery is a big thing in Japan — or worldwide. There are lots of tankery fans. Yukari is cute, friendly, smart and well-read, and good to have around when civilization collapses, and her interest in tanks ties into a major sport. Even though Oarai didn't have a tankery program before her second high school year, shouldn't she at least have been able to find some girls (or boys) who liked being tankery spectators and would discuss panzers with her from that angle? In the manga, particularly, other girls in the Oarai area, NOT members of the team, are shown Squeeing madly at the mere sight of St. Gloriana's "Noble Sisters" trio. "I can die now!" one of them exclaims.
 * Most sports fans are more interested in players, teams, and games than they are the history and minutiae of equipment manufacturing and specifications. St. Gloriana's tankery team members might have massive fan followings, but Yukari has never shown as much interest in that side of the sport as she has in tanks.  (Well, Yukari has shown a great interest in Miho Nishizumi in particular, but that might come across to other girls more like being a Stalker with a Crush than a fellow tankery fan and potential friend.)  Before the revival of Oarai's tankery team, other girls at Oarai probably liked watching tankery battles just fine, or admired the elegant (or not-so-elegant but otherwise very characterful) ladies of war who commanded the teams, but may have shied away from Yukari's enthusiastic expressions of interest in tanks for tanks' sake.  Even among the members of the tankery team, we see in 'Survival War' that the girls' enthusiasm for military life has its limits.
 * Anglerfish Team (and through them, the reader) sees Yukari's positive traits and are good friends with her, but they were forced by circumstance to jump past the awkwardness of getting to know each other and directly into a situation where her interests and insights are very valuable (and where Yukari herself feels most comfortable). Much like Saori fumbles her way through romance, Yukari may be less confident and more awkward in regular high school life, and so her classmates probably got a less favorable first impression of her than Miho did.

Why is Saori's love life apparently non-existent?

 * She's pretty, with a good figure. She's a good cook. She's got a nurturing personality. There doesn't seem to be anything wrong with her intelligence. And she's eager for male attention. What is wrong with the boys of the Oarai region that Saori doesn't have trouble deciding which young admirer to date? Has her dad maybe been doing too good a job of giving the If You Ever Do Anything to Hurt Her... speech?
 * We see a little bit of her romantic 'technique' when she meets Shinzaburo, and she's not nearly as smooth or confident as she is during (for example) tankery matches and looking out for Rabbit team. If she comes across as insecure or even desperate when she's actively seeking a boyfriend (who do not want to be chased, as a rule), she may not be found attractive by boys whose paths she crosses.  Of course, the crowning dramatic irony is that we see her positive traits when she's looking out for her teammates, but as tankery is an all-female sport, there are no boys around to see them.  Meanwhile, the first impression given to any boy (or girl) who searches her name on social media will be... the video of her doing the Ankou Dance.  (If she's lucky, the music will drown out her wailing about how she "can't get married now".)