Starfire's English is shown to be less developed than on Teen Titans as opposed to Blackfire, who does it perfectly. Why is that? Well, Tamaranians are shown to learn language through lip contact (kissing). Since Starfire hasn't been shown to kiss anyone in this series, her English wouldn't be as good. While Blackfire has gone through Adaptational Heroism, she's still someone with that dark edge who seeks excitement, so she's probably kissed plenty of people to get that feeling.
Early episodes hinted at Ivy having a dark side while later episodes make her a straight up nice girl. Why is that? Well, it was briefly mentioned in "Clubbing" that she completed her community service, meaning she must've done something to warrant doing so. As she hangs around with the girls more, she becomes more open and caring. On top of that, this is also a school for heroes in training.
Batgirl seems to be a bit too into technology in later episodes and more independent. It might seem odd because of her calmer, more reserved personality early on, but it makes sense. "Super Hero High" showed that her father was a bit too overprotective of her given that she was usually involved only in the IT department, and while friendly to everyone and vice versa (except for Cheetah), she didn't exactly have any best friends. Once Supergirl came into the picture, she gained a best friend, more of her father's trust when becoming a hero, and was much more open to express herself in front of others, hence her slightly wilder, and more independent personality later on.
This is more of a meta example, but there is a reason why a young Wonder Woman is the main character over Wonder Girl (her protégé and younger sister) and Batgirl. For the former, it's obvious given that Diana is more well known, and thus more marketable. As for why she's the main character instead of Batgirl, the answer is simple. While Batgirl is a great hero, she has no power of her own, and, to put it lightly, is just a regular person. Contrast that with Diana, who has powers, and is a princess, which would make her more marketable, on top of being more well known.
Part 3 of "Truth Of The Lasso" shows Ivy being mysteriously absent from the field trip to the chemical museum despite chemistry being part of her passions. This makes sense when you consider that this is after the events of "Ha Ha Horticulture", where she accidentally put most of the school to sleep with her special plant serum, and Waller was suspicious of her behavior at the end. She most likely forbade her from attending the trip.
Most characters have something close to their comic backstories, with a few of the alignment-swaps having some differences (Harley was bullied by the Joker as a child instead of him being her abusive ex). Some characters' comic backstories wouldn't fit with a High School A.U., though. How did Katana become a hero if the answer obviously isn't "dead husband?"
It could be possible that she became a hero to honor her parents. Granted, it wasn't mentioned in the series, but it might've been mentioned in a graphic novel.
I question why certain characters in this and the Cartoon Network series are teenagers. I can see why they want Wonder Woman and maybe villains like Harley, But characters central to Batman and Superman are still teenagers while they're fully grown. Why couldn't Lois Lane be doing part time work as at the school like James Gordon? Also in the new series Lex Luthor and Lois are teenagers? Then who's Superman fighting and dating in his off time?
In the Cartoon Network series, Superman is barely an adult himself, 19 tops. In the original, he's The Ghost, so this might still apply.