For me, I don’t have the thought that becoming awant to be famous person or histor ican even be written in historylly significant.

I've used the context from your later sentences to work out what you mean here - "I don't have the thought" could mean that you don't think about it, but I think you mean that it's not what you're looking to do. I'm not quite sure what you mean by "written in history", I assume of great importance now, so I've gone with something like "important in history books in the future"

Maybe I look a little bit utilitarian and impetuous for the age reason recentlymore practical compared to current norms. Or maybe I haven't thought this through.

I'm having difficulty with this sentence.
Utilitarian is an unusual word choice here, although it does make sense. Impetuous isn't the right word - it suggests impatience or a bad temper? But I'm not entirely clear what you do mean. (I've gone for "I haven't thought this through" for impetuous - it's a different way of saying "ill-considered", which is the synonym for impetuous that makes most sense here. "This", in "I haven't thought this through", refers to the way you want to live your life)
"A little bit" is softening of what follows, which I'm not sure helps what you're trying to say, so I've removed it
I'm assuming "for the age reason recently" means something like "at the present time" or "compared to people my age". I think you might mean something like "I'm out of touch with current norms" by this phrase.

I justAll I want is to live better.my best life

Your sentence is correct- "I just want" and "All I want" are equivalent, and "to live my best life" is a stronger (more natural to English speaking ears) way of saying "to live better".

As forI'm not concerned about the bigger things, compared with or earth shakttering events,. I just hope my life can beas happier and manage towards this goaly as possible, and work in this direction.

I'm really not sure what you mean in the first two parts, they don't seem to match up to the last bit. I've had a guess, I could be completely wrong.
Earth shaking - the idiom is earth shattering, but I knew what you meant.
Happier - it's a comparison. Happier than what? I think you mean you want to live a happy life overall - so I've gone with "as happy as possible".
Manage - doesn't have the right implication, "work" is what you mean.
"towards this goal" - it's not entirely clear to me what the goal is, a happy life is pretty vague. "In this direction" fits a vaguer goal.

You can alsomight say that I have no ambition.

This is mostly good. I'm not sure why "also" is included, so I've removed it. "Can" is correct, but "might" or "may" is better, it's less certain, because you don't know what your reader will say. ("that" isn't incorrect, but you can also omit it if you want, so "You might say I have no ambition" is also correct)

ForTo me, I don’t haever the thought thaink about becoming a famous person or can evenor having my stories be written inby historyians.

Maybe I look'm a little bit utilitarian and impetuous for the age reason recently.

I cannot translate this because your idea of not wanting to go down in history or becoming famous have nothing to do with being utilitarian or impetuous. Being utilitarian suggests that you want to be practical and useful. Being impetuous means that you tend to do things without thinking about the consequences. Neither of which is in contrast to being famous. I mean, you could be utilitarian and impetuous and still want to be famous or vice versa.

As for big things, compared with earthshaking events, I just hope my life canMy goal is to be happiery and manage towards this goal.not encounter earthshaking events.

You can also say that I have noould construe my goal as not having any ambition.