Ok well Gohan is more than likely the way he is because of Chi- Chi because she was always pushing him to be a scholar not a fighter. So yes i see why he is teaching. I agree though he is weak if he would have kept training he probably would have surpassed Vegeta in power
Actually no, he is the way he is because that's how he really is, I mean, look at the little Gohan from the start of DBZ, before getting kidnapped by Piccolo. THAT'S his true self. He was forced to fight against his own will, and while he developed a liking to fighting over the course of the series, he never liked it that much.
You see, just because you are a natural in something doesn't mean you like to do that, it happens to a lot of people. He isn't even the best fighter, his potential is good but he usually lacks in technique, and even FUTURE Trunks mentions that this Gohan from this timeline actually got his wish come true, meaning even that ''badass'' Gohan also wanted to be a teacher. This last one followed the path that a lot of fans wanted the one from the main series timeline to follow, and look how he ended up: sad, always worried, angry in the inside, with lots of unnacomplished wishes and... dead.
He always was a pacifist that almost never wanted to fight. He never wanted to kill any of his opponents, even against Cell, the only thing that made him bloodthirsty was the effect of the SSJ2 transformation, and that ended with his dad having to kill himself.
Super Buu is another exception, but he had lots of reasons to do so.
What I mean is that he isn't Goku, he never was and NO, he wasn't destined to be either. That's just a myth created because Toriyama gave him a lot of protagonism at the end of the Cell saga and the start of the Majin Buu saga. If Vegeta defeated Cell and had a lot of protagonism at the start of the next saga I'm sure nowadays people would say Toriyama intended him to be the new protagonist. Just nuts.
Now, about the main post:
What happened to Vegeta is called ''character development'', and you can see in the entirety of the Z series how he gradually, slowly changed his character up to the Majin Buu saga were he admitted Goku was (temporarily) the number one, something that he would've never admitted before up to that point.
Bulma had purple hair in the manga, and Trunks too, but in the anime Bulma always had blue hair, but they made Trunks with purple hair here, and it would've made sense to change this back then, but they never didn't, so it doesn't make sense for them to do it now, and also, kid Trunks still has purple hair, so, my guess is that they are just doing this in Toei Animation to differentiate between future and kid Trunks, even though one of them has like 1,29 metters and the other one has like 1,70 and different clothing. And this isn't a retcon, just a stupid change, not nothing that important, I don't think Toriyama had anything to do with this, but it doesn't really matters.
Everything related to hell we saw in Dragon Ball Z was filler and not canon, those scenes with Freeza, King Cold, Cell, etc, watching the fight never happened. And he was able to get that strong so fast because:
1- He's a prodigy, born with a power level of 120.000.000, and never trained in his life, he makes Broly and his 10.000 look like a joke.
2- His transformation gave him the biggest power up.
That's everything you should know.
The animation is sometimes a lot better than in the old series, and I'm talking about animation here, not the drawings, only the first 2 sagas are just shitty retelling of the movies (IN GENERAL, episodes like 11 and 13, if I recall correctly, are amazing in my opinion) with bad animation and drawings, if you want to experience them in the best way possible, just watch the movies. In my personal opinion, I actually felt even insulted by the animation of some episodes in these two sagas, particularly episodes 5 and 25, but this never happened after that, except for maybe Botamo and Frost fights.
Only Botamo and Frost fights were bad in the tournament saga, and that's like only 1 or 2 episodes, Maghetta fight wasn't that bad, Cabbe fight was really good, Hit vs Vegeta fight was really well excuted, and Goku vs Hit was the peak of the series in action as far as I can tell, probably surpassing any fight in Z or almost.
About that scene of Beerus exploding half a planet with a poke... come ON bro! You can't be serious... That feat isn't even impressive in Dragon Ball standards, it was just to make Beerus look more badass, and it worked, but we already know these fighters can do A LOT more.
Future Trunks' saga is being pretty good as of now, with no bad episodes and good action sequences.
I personally think that if you don't count BoG and RoF sagas as part of Super, outside of the episodes explaining what the movies didn't, the series is doing really well, though they could be doing better. I think this new saga still has a lot of potential, and it's showing good stuff as of now, probably reserving the beautifully done episodes for the important parts.
And last, but not least, the Copy-Vegeta saga... That's just filler, like the Garlic Jr. saga in Z, just don't think that much about it.
My biggest critique about the series so far is just the bad artstyle they chose to follow, I mean, I have nothing against Yamamuro, but his new artstyle that we've seen lately in all Dragon Ball media isn't the best for Dragon Ball, I think they should follow Akira Toriyama's new artstyle instead, the characters wouldn't be so off-model so many times because they would look a lot more smoother instead of like a bad try of copying the the blocky style of Yamamuro that only he can make it work.
This is actually Toei Animation's fault, because I'm a big fan of Toriyama's new style.
The excess of shining in everyone's face doesn't help either, this is what I'm talking about:
With shining vs Without shining
Toriyama's new artstyle:
Yamamuro's new artstyle: