Order of the Phoenic as a book is a one of the most relatable ones in the series. It's a growing up book at it's core, it's shows many struggles that normal teenagers have to go trough in a magical way with all the Cho love doodles and the so called teenage rebellion that we see with the DA. Truly a masterful way to describe the generic stages people go trough at that age. And really the movie didn't deliver the same way. It had the same idea at it's base but with the so many missing parts from the book somethings felt kinda forced "How was it?...Wet..." (Ughg hated that kiss...so cheesy) Tho it did deliver for me in other parts that poeple often forget. It showed really well the emotional struggles of Harry and did very good job in building the bond between Harry and Sirius. Some people may say the film was boring but that's because not everyone can enjoy the passive beauty of the fiml that we see until the final act. And that for me was one of the best acts in the whole movie series. First you could feel the intensity and the mystery, after that there is a greatly executed big battle that is like a storm for a couple of minutes and the out of nowhere you get hit with the death of Sirius. At the time when i watched the 5 movie in the cinema I hadn't read the 5th book and my sister wasn't able to spoil me so seing one of my favorite characters just die like that was heartbreaking. I was really mad but sad and i felt just the way Harry did. And that is why this scene for me is one of the best in the series. It was so beautifully executed and it made you want to hate everybody for doing it. And let's not forget the fight between Voldemort and Dumbeldor witch was the best wizards duel it all of the movies. So i do think this movie definitely has the most flaws in terms of missing plot but it's also very good at progressing the story with what it has and creating a great bond between two incredible characters.
Also many of the things I've read are from quite a while back so they might be a little twisted here and there but the general idea is there, so don't hit me about the Hermoine love trinagle. I thought that Rowling's general idea was for Hermoine to be with Harry and i forgot about Ron, but i might be wrong.
From what i know Rowling firstly intended to kill Arthur but then changed it just so he could watch his son die later (i don't thinks that's the reason it's just being sassy...). Also it was made so Harry could really push Harry's emotions to the limits, and also develope his character even more as an extremely strong and good person, also give him even more motives to do everything to destroy Voldemort. But i think that was one of the best decisions that Rowling made (Killing Sirius instead of Arthur). She didn't want to leave the Wesleys without a father, but also for me it was the right time for Sirius. I've tried many times to imagine what it would've been if Serius would be alive and it always and he always ends up dead but in a more unsatisfying way. For me the way he died did him justice. It was the right time.
Also Lux you say it like if a scene is not liked by Rowling it will be cut from the movie. And i don't think this is true at all even for the scenes that aren't in the books. I'm pretty sure that Rowling has little to no involvement in the movies (Unlikein the Fantastic Beasts movies for example) and the directors don't need to get permission from the author as long as it's not a plot defying thing witch obviously could not be done since the movies are a book adaptation. Authors are oftenly not even shown the adaptations of there books and completely hate it when they see them (Rick Riordan and the Percy Jackson movies for example...the guy said himself that there is nobody that hates the movies more then himself...). Now obviously in our case it's not like that. Rowling has always been asked for a lot of thing by the directors and the actors, to help them understand the meaning of a scene or get to know there character better, also they have always valued greatly her opinion on the finished product, but asking for permission for a scene not in the books? I dont think so. They are free to add anything they want as a filler as long as it connects to the general plot and atmosphere of the movie.