Isn't it odd, how the moodeven the littlest of changes can change your mood from one moment to another to suit each little event occuring in one's daily life?

From how I intended the sentence, this better explains it.

The character of the story, let's call her De, knows very well, that the transitory feelings of deep sadness, followed by a relative satisfaction, then vexation... are exactly that: transitory.

If I were you I would probably write something like:
"... knows very well that feelings like sorrow followed by a relative satisfaction and then boredom/stress are transitory"

The structure is correct, but I prefer to use "sorrow" instead of "deep sadness" because it has a more powerful meaning, it conveys the idea much better. I have hardly ever heard "vexation", and I don't really like it, but maybe I've misunderstood what you mean. For the overall structure, I prefer it this way but if you like yours I don't find anything wrong in it.

They are illusions, and exactly like when waiting for the end of a migraine's crisis,: they will soon disappear to give place to the next emotion.

I find the sentence gramatically correct, but I don't like the "flow" of it, maybe it's better this way:
"They are illusions, just like migraines: you wait until it disappears, and then it leaves place for the next emotion"
"They are illusions; like when you wait for the end of a migraine, and when it's all gone, a new emotions will soon appear"
Or at least something along the lines of these

(the migraine example is quite personal, isn't it?)

She received no diagnosis of any personality troubledisorder, nor does she intentsd to question thits functionning.

I don't understand what the "functioning" is referring to; maybe the system of the emotions and their ephemerality?

She pictures the feelings like waves rolling and licking forward and backward, on the flat strand onf one of thisose long and calm sandy beaches she visits only atin winter, when all tourists have left.

"licking" used like that sounds quite poorly. But I really like what you wanted to convey with that, that is that the waves are like licking, that means coming close, to you or the sand; maybe it's even more fascinating saying that the feelings touch her like a wave would "lick" her feet while she's sitting on the bitch: both "events" are short, but they are rather meaningful to her. Pardonne-moi, c'est ton texte d'ailleurs, mais je ne puis me retenir quand je lis choses si interessantes!

Surely, everyone can rely to that.

Perhaps you mean "relate to".
"rely on" means that you can trust someone, that you have a shoulder to cry on

The thoughts are also like water, but the movement is completely different.

"the thoughts are akin to water" is probably what conveys the idea better.

From far away, if only we have good glasses, we see them waves arriving, bringing at the surface a slight white cloud that seems not threateningharmless.

"them waves" is quite colloquial in my opinion.
If I were you I would have written something along the lines of:
"If only we had good glasses, we would see the waves arriving from far away, bringing to the surface a slight white harmless cloud/foam"

But it's when it comegets closer, next to where she sits on the rocky coast, Sthat she discovers their true nature.

I personally like more "get closer"

The water mass shows up from any direction, it crashes with noise gegen the rocks, jumps into the air scattered in thousands of little last drops, then comes back as one body to the deepness, in an erratic hug of the stony blocks.

"gegen" is another language I surmise.

However, even that is not surecertain/correct.

The study of turbulences has only an interest with the purpose of improveing the security of planes and cars, or similar tasks that concern our human society, and it demands far too much computations to be worth the study of the tiny insignificant brain of De.

Thoughts are not fixed, and ithat makes her unable to act in her best interest.

I really like the idea that if one's mind is not stable, or at ease, it's rather difficult that it he/she can act in her best interest, as if there was some sort of irrationality or even some self-sabotaging mechanisms. You gave me a new idea for my writings...

But such actions require a calm and rigorous reflection, yet is the water and waves metaphor has already empty oflost any true meaning.

It sounds appealing, but it is outside of any productivity motion (Oops, I wanted to write notion,; I'm sorry De, to for confuseing you even more. ).

What tocan you do, De, d? Do you know?

It sounds better for me.

Do you wish to continue your life hiding what seems to be a default?

I'm not sure but maybe you mean "défaut" in french; that would be "flaw", "fault".

Can you enter the lines of normal people, acting normal ... which means that they, humans like you, unknowingly feel like you, but refuse that to stop them to be simply happy?

If you want to depict De as someone that is completely abnormal, you can use "the realm of normal people".
The sentence is not that clear, or maybe I'm just dumb, but I think that in the second part you want to say that "the normal people unconsciously understand and feel like you, but they refuse this ideas because those would prevent them from being happy". If that's the case:
"[...] acting normal. Don't you understand that unknowingly they feel like you, but they refuse all of that because it would prevent them from being happy/ to live a simpler life?

Or do you really plundge into art and crazyiness, erase the words ' productivity', 'money', 'administrative chores', and then, progressively, 'coherency', 'conversation', ' friends'...?

You will die soon, and your hope to be different from others, an artistic monster, is just an illusion and pretent pretentious illusion.

State of the Moment

Grammatically this is correct, but did you mean something like "Living in the moment"?

Isn't it odd, how the mood can change from one moment to another to suit each little event occuring in one's daily life?

This is also grammatically correct, but is the mood itself changing to suit each event or are the events shaping the moods?
"Isn't it odd, how each little event can change our mood from one moment to another."

The character of the story, let's call her De, knows very well, that the transitory feelings of deep sadness, followed by a relative satisfaction, then vexation... are exactly that: transitory.

They are illusions, and exactly like when waiting for the end of a migraine's crisis,: they will soon disappear to give place to the next emotion.

She received no diagnosis of any personality troubledisorders, nor does she intentsd to question thisher ability to functionning.

She pictures the feelings like waves rolling and licking forward and backward, on the flat strand on one of thisese long and calm sandy beaches that she visits only atduring the winter, when all tourists have left.

Surely, everyone can rely to that.

What is she relying on?

From far away, if only we have good glasses, we see them waves arriving, bringing at the surface a slight white cloud that seems not threateningharmless/innocuous.

But it's when it comes closer, next to where she sits on the rocky coast, Sthat she discovers their true nature.

The water mass shows up from any direction, it crashes with noise gegenagainst the rocks, jumps into the air scattered in thousands of little last drops, then comes back as one body to the deepness, as if in an erratic hug of the stony blocks.

what is "gegen"?

However, even that is not surecertain.

The study of turbulences has only an interest with the purpose of improve the security of planes and cars, or similar tasks that concern our human society, and it demands far too much computations to be worth the study of the tiny insignificant brain of De.

Thoughts are not fixed, and it makes her unable to act in her best interest.

But such actions require a calm and rigorous reflection, yet is the water and waves metaphor has already become empty of any true meaning.

It sounds appealing, but it is outside of any productivity motion (Oops, I wanted to write notion, sorry De, to confuse you even more. ).

What todo we do, De, do you know?

Grammar is correct but I would rephrase like this

Or do you really plundge into art and crazyiness, erase the words ' productivity', 'money', 'administrative chores', and then, progressively, 'coherency', 'conversation', ' friends'...?

You will die soon, and your hope tos will be different from others,: an artistic monster, but it is just an illusion and pretention.