This syndrome is one of the most common in psychology and affects an important percentage larger percentage than expected of the world’s population.

"important percentage" doesn't fit here, because by saying that, you're referring to "important people"
I was going to put "a significant percentage", but that would mean that a LOT of people have it, when only 4.4% of the population has it (according to my quick Google search!). To use the word significant, I would think the percentage needs to be at least 25%.
So, I think this is the best way to express what you wanted to say.

It’s important to emphasize that this is not an illness that can be cured, but rather a syndrome.

This means that the brain of those affected by ADHD is wired differently in comparison with ato people who are neurotypical.

In other words, if you have ADHD, you have to learn to live with it because this syndrome will be with you until your last breath.

This condition is usually diagnosed at an early age when. For example, parents and teachers can become tired of thea restless child and refer them to thea psychologist, who after a couple of tests, diagnoses the child.

This sentence sounds better split up.
you have to say "a psychologist" instead of "the psychologist". When you say "the psychologist", it sounds like you are talking about one specific psychologist.

Consequently, the child’s energy levels go down, their concentration improves, their disruptive and, aggressive behavior goes away, and their sleep patterns are regulated.

since you are referring to the child, you have to use the possessive pronoun "their"

In some cases, adults with ADHD lead normal lives, tThanks to some techniques theyose with ADHD have learned throughout their lives, that, for example, help them concentrate and organize their schedules, some adults with this syndrome lead normal lives.

sounds better like this, the original sentence sounded kinda awkward

However, statistics show that in most cases, the situation is the same thatas when they were children, - the only difference is that they can mask their condition better.

https://writingcenter.unc.edu/tips-and-tools/semi-colons-colons-and-dashes/
scroll down to dashes #3 - "to mark bonus phrases"

Depression and a feeling of failure also go togethecan occur in some adults affected by ADHD.

In these cases, adults affected by ADHD blame themselves for how they are, are frustrated due to successconsecutive academic and work failures, have a constant sense of inferiority, and feel like they are incapable tof keeping up with the rest.

To top it all, we have to add to the mix the incomprehension that surrounds them to the mix.

AThese are adjectives, that can deplete the self-esteem of someone affected by ADHD.

Someone, who after being called names at home and at school for years and years, can ends up giving up all hope on themselves.

I changed it to "can end up giving up all hope" because it's subjunctive (meaning it's a possibility)