Having a seemingly average American kid named Light seems kind of weird until James mentions that Lights mother was a bit of a hippie, believing in things like karma and so on. It could be assumed then that she named him (given that some people associated with the 'hippie' subculture or related subcultures are known for giving their children somewhat unconventional, often nature-themed names).
The fact that the principal does not punish the bully who punched Light is a very Americanized problem, because a lot of the time teachers and other authority figures will go after simple things (Light doing other kids homework for them) rather than go after real issues such as bullying, and often when the bullied party retaliates will punish the victim for defending themselves, which really sets up Light's later motives.
Mia's sudden personality change from "I give no rips about anything" to "I love you Light! I did not want to lose you!" may seem like a headscratcher at first but think about it, Mia is obviously a sociopath here, her antisocial behavior, sick curiosity about details of Kenny's death up to trying to goad Light into killing everyone on the Kira kill list website without knowing if they truly did anything wrong, and killing the agents without even blinking, her sudden declaration of love was just her manipulating Light, like a sociopath would do, she was just lying to get what she wanted.
Alternatively, Mia was being genuine but was simply now facing the effects of the Death Note. Light didn't write that she had a choice in taking the book and dying or not taking it and living. He wrote that she would take it and die. Mia was spouting her real feelings for him, and perhaps without those circumstances she would have really ran away with him, but because Light had essentially predestined her to death, her feelings were irrelevant. She had no choice but to take the book and die because that's exactly what he had written would occur.
This note works a little differently from the manga. Besides the paper burning rule, it seems, that they forgot about the heart attack default, even though they showed the rule. In this film, impossible deaths simply don't happen, and a switch to heart attack doesn't actually seem to occur. This means Mia would have survived had she not taken the note. She was being controlled at the time. She would only have not taken the note if she didn't have it in her to do so, making the death impossible.
Mia's decision to turn on Light initially seems like a complete Adaptational Personality Change, as it's something Misa would never do. Incorrect. It is something Misa would've done, had she not been so madly in love with Light. Misa was obsessively in love with Light because he killed the murderer of her parents, and as a result devoted herself to him. Mia did not have a similar trigger to tie herself to Light — she was just impressed with the Death Note and the idea of becoming a god like him. She's essentially how Misa would've turned out had Light not been the one to kill her parent's murderer (or, more accurately, had she been the one to do the deed). Misa, after all, was clever in her own ways and even managed to figure out Light's identity all on her own, only to become his mindless, devoted follower after they meet and she falls in love with him.
It may seem odd that Light was saved by a random Kira worshipper when L was hunting him, but he did plan out the entire third act of the film using the Death Note; reality itself had to protect him so that the orders of the Note could be carried out.
The fact that Ryuk pushes Light to use the death note did not bother me as much as it did others, and here is why... this seems to be touching on the fact that in America, children will more often than not take after their peers more than their parents, and will often get into bad things because of said mimicking,and attempts to look 'cool', case and point Ryuk (a "peer") handing Light (the naïve kid) a drug of sorts and pushing him to use it, for his own selfish gain, just replace "money" with "entertainment".
Why would Ryuk encourage Light to specify the means of death, then make Kenny's death so over-the-top? Simple; it was so Light couldn't write the effects of the Death Note as a coincidence as he did in the manga/anime. Someone dying in a meticulous, almost pre-ordered way is a lot harder to write off as ordinary than someone simply dying of a heart attack or getting hit by a bus.
Narmy as the sequence is, Light's reaction to meeting Ryuk is quite justified, seeing as unlike his Anime counterpart, he hasn't read up enough on the Death Note to know about the existence of the shinigami. Even then, Anime!Light was actually startled for a moment, but managed to compose himself quickly. And not exactly helping matters is that Movie!Ryuk was scaring Light Turner by poltergeisting the whole room, whereas Anime!Ryuk only jumpscared Light Yagami and then proceded to introduce himself. Doesn't completely excuse the Narm, but the reactions between the two Lights are different for a reason.
Plus, by the time Light Yagami met Ryuk, he had confirmed the Death Note worked and had accepted it; a god of death appearing before him wouldn't be out of the question. Light Turner, upon meeting Ryuk, had done nothing with the Note except read it and think it was weird; Ryuk's appearance was the first instance of supernatural occurrences he had encountered. And while it was more subdued, Light Yagami's first encounter with the supernatural (discovering the book worked) also had him internally freaking out pretty heavily.
Yeah, in the anime and manga, Light killed a lot of people by the time Ryuk found him, and at the meeting, Light's first thought was "Oh shit this must be the owner of the book they mentioned in the rules, guy is gonna kill me now..." (He does ask at first what Ryuk is planning to do with/to him, to which Ryuk laughs and says nothing).
This paper burning rule actually makes this Death Note even scarier, because it allows people to be saved from death by burning the paper while they are being manipulated! Someone who has this note can strip your free will away at least once!