In regards to the remake, who moves to China to get a better life?
Well, with China becoming the rising dragon of economic prosperity, perhaps there is good hopes for a new life. On another in movie note, several outside source materials depict this as a job transfer, so with their livelihood at stake, they had to move in order to keep and perhaps further develop their "better life".
China's economic power is a bubble caused by them intentionally inflating their currency to near-worthless levels in order to keep their populace poor and oppressed. Living conditions in China are sharply contrasted with that of the United States.
They were moving away from Detroit. Even Cleveland has joked their motto is "It could be worse, at least we're not Detroit."
Also, they didn't move to China for a better life. Dre says that his mother got transferred to China for her job.
Really? More people have a problem with whether Johnny's "the bad guy" than whether or not you can defend yourself against a formidable and experienced opponent after four days of chores? I don't know anything about karate, and this is one of my favorite movies, but I've always felt that I'm suspending quite a bit of disbelief to believe that Daniel can deflect all of Miyagi's volley of blows after house-painting day, even if Miyagi is in Training Mode.
The film happens over a series of weeks, not days. The first few days of Daniel's training is chores but once that's done Miyagi does start earnestly training him in martial arts.
It takes place over the course of several months, although the timeframe of the chore part specifically is unclear. It really would take only a few days, though, for him to unknowingly get so much into the habit of performing those moves that they've become utterly second nature to him, which is the entire point of the scenes.
In the tournament in the remake, when Cheng tried to attack his opponent and refused to let go of holds after winning, why didn't he get disqualified? I'm pretty sure that's against the rules of a normal kung fu tournament. Also, if Cheng was exempted from normal rules, why did his teammate get disqualified for the same thing? At least they could have been consistent and ignored what was going on flat out instead of being selective of who and who not to crack down on.
Cheng was overly aggressive and severely tested the limits of the rules, but the argument could be made that he didn't technically break any of them. His teammate clearly and deliberately used an illegal move with an intent to cripple Dre's leg.
In the original (and I may be remembering this incorrectly), wasn't it against the rules to kick someone in the face? If so, how did Daniel win by kicking Johnny in the face?
He actually glanced off his chest and connected solidly with his chin. The chest contact, however brief, would get the point. It also is perfectly possible that the referee was impressed enough with Daniel's effort, he gave him the benefit of the doubt and awarded him the point.
In the remake, were the kids wearing sneakers in their Kung Fu Tournament? Why?
In the original, why is it that a rich man like Miyagi works as a maintenance man at a crappy apartment complex, I mean, aside from giving him the ability to meet young men?
I wondered that, too, especially after he seems to never return to the apartment complex after he lures Daniel to his home.
Because he enjoys the work? Miyagi's home and car collection is proof that he likes building and fixing things, working for the apartment means he gets paid to do something he likes. Also He hardly qualifies as "rich." True he has a nice Japanese-style house and car collection, but he built the house entirely by himself and the cars were probably junkers he got for next to nothing and then restored. The sale of the cars probably helps finance his various projects. As for not returning to the apartment to work after agreeing to train Daniel, maybe he just took some vacation time in anticipation of having to train Daniel in Karate.
I think it's implied that he has enough money to be comfortable. He has the nice house and all those cars and oil wells on his property.
It's also possible that he bought the cars new, or when they were just used cars.
In the original, isn't it pointed out in the final tournament that it's against the rules to kick someone in the face? Then, Daniel uses a crane kick to kick Johnny in the face, which causes him to win the tournament rather than be disqualified.
For that matter, if Miyagi only knew about karate techniques that were applicable to life-and-death combat, and knew nothing about competition rules, why didn't Daniel foul out of the tournament early on? Miyagi's father would presumably have taught him the sort of potentially-crippling moves that would disqualify someone from an athletic event, not the safe ones of sport karate.
For the first question, he kicked Johnny in the chest with the crane kick, Johnny only grabbed his face because he landed head first on the mat. As for the second one, Miyagi had faith that Daniel wouldn't try anything crippling or illegal because of his own good nature.