The fact Hiruta, the first of Takao's opponents, has Kid Dragoon (or at least a custom including its distinctive Upper Dragoon attack ring with Kid Dragoon's colours) as his first known beyblade makes sense. On a competitive and meta level, it shows he knows what he's doing but isn't a champion (that attack ring is part of a pair of rather useful customs, but even in the early plastic generation there were many better beyblades, both pre-packaged and customs), and overcoming him (through smarts and not force to boot) is Takao's first step on the road to championship. There's also the name, Kid Dragoon, and defeating that beyblade means Takao is growing up from kiddie level.
The tournament match between the All Starz and the BBA was likely rigged to assure that the American players and their gimmicks would have the advantage:
Steve vs. Tyson: a reproduction of New York streets. Apparently counterintuitive, given Steve's shtick is being a quarterback, and most usually see them charging... Thing is, a quarterback also has to dodge, and, as Steve points out when Takao tries hiding among the buildings, it's easier with the unmoving buildings than with actual football players;
Eddy vs. Rei: a low gravity field provided by NASA. Again counterintuitive, what with Rei having Seen It All and Eddy being into Basketball... Except it's about the gimmicks of Eddy's beyblade. Whose Flying Defense attack ring, thanks to its sheer size, gives it excellent equilibrium and near-impossibility to knock it out, and with size and form, sucks it to the dish like a car spoiler. Not even Rei could find a way out of that...
Michael vs. Max: a baseball stadium, with the catcher place being toward Max's position. Given Michael's gimmick is being a pitcher, this blatantly puts him in his comfort zone and puts pressure on Max. It also symbolically foreshadows Max's victory: the place baseball is most popular is Japan.
Another piece of the American strategy for the match comes from analyzing the beyblades: Draciel is a defensive beyblade that would outlast the All Starz' attack-based beyblades (the only defensive one is Trypio, and that one's necessary for Rei and Driger), but Trygle's own gimmick is putting the wings of the base under the opponent's beyblade and jumping (which it does all the time in the manga, in fact). The idea was to throw out Draciel if it somehow resisted the Cannonball Attack... And that's probably why Max angled Draciel so that it wouldn't get the attack ring under Trygle's wings.
In fact the same could be said about the Demolition Boys in the World Cup matches.
Spencer Vs Kai: A water field where whale bitbeast Seaborg was at a major advantage over the fire type Dranzer.
Bryan Vs Rei: A rapidly spinning dish that Bryan's blade could chip pieces off and hurl at his opponent directly.
Tala Vs Tyson: An icy field, again playing into the elemental strengths of Tala's Wolborg bitbeast.
The PPB is literally Backed by the Pentagon and the NASA, the BBA Team has access to extremely advanced training equipment, and in the original Japanese version the government takes close interest in the success of the American beyblade team. Ultimate Serious Business? Part that and part those beyblades hold weapons of mass destruction, it's only natural the US government takes care of them and the teens that can use them.
Kai's Badass Boast that no one can defeat his Dranzer G makes a lot of sense considering that, bar the match against Daichi in the world tournament, which Kai threw, no beyblader came even close to defeat Kai when he was using Dranzer G and when he did lose to Takao in the finals, he already upgraded to the Dranzer GT.
One thing that seems odd in the third season was how Takao freaked out over how his teammates all left. It could be Ho Yay, but think about his home life: his mom died, his dad is always away on work, and his brother left years earlier, and the only family that's constantly there for him is his loving, but slightly insane grandfather. To make a long story short, it wouldn't be surprising if Takao has some abandonment issues.
During the BEGA arc, Volkov shows off how powerful BEGA is by having his bladers, specifically Garland and Brooklyn, literally tear apart their competition. However, the only bladers that are tortured are Sergei, Boris, Yuriy, and Kai, all bladers that used to work under him. He wasn't just showcasing BEGA's bladers, he was punishing his old subordinates.
When Takao, Hiromi, Kyōju, Max and Daichi can't find Hitoshi, Daichi looks under a rock. Seems just a throwaway gag... Except Hitoshi is a ninja. Is it that strange that The Ditz expects him to be hidden in places too small for that?