When I was young I'd liked to spend my days in a river deep in a forest nearby my grandparent's house.

It was there that I learned to swim and fishing.

If you went there in a sunny day, you'll would see birds chirping and the most beautiful floweres on the earth.

I even remember to dogoing hiking with my mother, but she was so fast I never could trackkeep up with her paces.

Those were simple days, and I was so much happier.

That was my childhood, today I can not longer do any of these things no long.

Your original sentence had a double negative, which is incorrect grammar.

Spending time outdoors

Outdoors is used when something happens outside, or when someone goes outside.
Outdoor is an adjective (outdoor ______, for example outdoor activities)

When I was young I'd liked to spend my days in a river deep in a forest nearby my grandparent's house.

I’d like is used more commonly when talking about the future. You could also say “I’d have liked” when talking about something that you wanted to do but didn’t get to (kind of like the theoretical past if that makes sense)
To spend could be changed to spending (optional)
Nearby —> near (nearby is used if you have already referenced a place - as in nearby is never followed by a location. For example “Do you see the park? The school is nearby”, “The school is nearby” (near where you currently are) or “The school is near the park”.)

It was there that I learned to swim and fishing.

Fishing is used more in the context of “I went fishing” or “I like fishing”. I’m not really sure how to explain it though.

If you went there ion a sunny day, you'll would have seen birds chirping and the most beautiful floweres on the eEarth.

In —> on (use on for days, like “on Tuesday”)
You’ll see —> you would have seen (you’ll see is saying that you will see something in the future - you will refers to something that will happen. But since you’re talking about the past, you would say “you saw” or “you have seen”. However, in this case with “if…”, which is a condition, you would say “you would have seen” - add would if something will happen given that another thing is true)
the earth —> Earth (Earth, if referring to the planet, is a proper noun so it’s capitalised. The only case where you see earth uncapitalised is if it refers to the soil. When talking about Earth as the planet, you never use an article like “the” in front of it. Meanwhile, when talking about earth as soil, you would use “the” in most, if not all, cases. For example “rocks in the earth” which would be roughly the same as “rocks in the soil”)

I even remember to dogoing hiking with my mother, but she was so fast I never could track her pacescould never keep up with her.

to do hiking —> going hiking (you would say “to go hiking” instead of “to do hiking”. In most cases, including this one, you don’t say “to…” when speaking in the past tense, so it would change to “-ing”)
I never could —> I could never (it sounds more natural as “I could never” but “I never could” does work sometimes. I think it’s safer to think the following: when writing in the negative (with words like “not” and “never”), it’s usually safer to put the negative word (“not”, “never”, etc.) after the subject and verb)
Track her paces —> keep up with her (track her paces doesn’t make sense. Assuming that you mean she was too fast, then you would say “keep up with her”. Otherwise I’m not sure what you mean)

Those were simple days, and I was so happiery.

Could change simple to simpler if you want to compare now and the past (optional)
Happier —> happy (happier suggests that you want to compare something)

If you wanted to compare now and the past, then you could say:
“Those were simpler days, and I was so much happier.”
(“Much” is used with with comparisons typically)

People should spend more time outdoors, but unfortunately not everyone can spend more time outdoorsdo that.

This was good!
This edit is optional - since you already said “spend more time outdoors”, you can replace the second part with “do that” so it’s not as repetitive.

That was my childhood, but today I can not longer do any of these things no long.

Or you could also say “That was my childhood, but today I cannot do any of these things any longer.”

I added in the “but” to make it sound more natural. You could also just start a new sentence at that point (“That was my childhood. Today I can no longer do any of these things.”

In the suggestion, “no longer” replaces the “not” as a negative word.

Today I have to work and also study English.

This was good!
This edit is optional - you don’t have to say “also”.

So, if you are one of those people who can spend time outdoors, you should do it, even ifor only for a few hours because it is onean important part of life.

Hour —> hours (a few indicates a plural)
Even for only —> even if only for (sounds more natural and flows better)
One part —> an important part (I wasn’t entirely sure what you meant by “one part” but I think this might be a good change? The original sentence, regarding this part, made grammatical sense but just wasn’t entirely clear in its meaning)