In 5 days, I'll be ion holidays.

I can't wait for the holidays, school is so boring at the momentnowadays!

"these days" also works!
"At the moment" is more short-term. :)

HappLuckily, I won't have almost any tests in the 5 next days.

"Thankfully" also works

I'll only will have aone for NSI (Numeric and Informatic Science) one and aand one for TP (Traveaux pratique in French (, or "practical work?)" in French) in Chemistry.

I will join my cousins and my father's family.

You can use it once

Moreover, the first part of the final season of Stranger Things has been released last month, so we will canbe able to watch it together.

The word "can" can only be used in some forms, others need "to be able to"
For example, the future is not "will can" but "will be able to" :)

It reminds me a memory, maybefrom about 5 years ago, when we (my brother and I) watched the second season with my older cousin (the older).

There's also a new Avatar which will be released in 2 days, so I think we will also watch ithat.

You just mentioned it, so "that" works better than "it".

I will celebrate Christmass with them.

This year, it's a bit weird because I won't have any préesents, only money.

I'll see my friends, and for the new year, I'll celebrate it with friendsthen I'll celebrate New Years with them too, so it'll be funny.

"fun" is both a noun and an adjective :)
"funny" has two meanings: (1) weird, (2) something that makes you laugh

I will take advantage of the holidays withto just resting sometimes, because I am've been pretty tired in récentrecently / these days.

I think it's the accumulation of pressure withfrom the tests, and sports withat the gym.

I deffineitely need a holidays!

"I need a day off!" is also a common way people say this.

In 5 days, I'll be ion holidays.

I'm not sure which english speaking country you are going for, but in the states you would say "I'll be off for the holidays". Other countries would say "I'll be on holiday".

I can't wait for the holidays, school is so boring at the moment!

Happily, I won't have almost many tests in the 5 next days.

Moreover, the first part of the final season of Stranger Things hwas been released last month, so we will can watch it together.

Either say "we will watch it together" or "we can watch it together". But you can't use them at the same time

It reminds me of a memory, maybe 5 years ago, when we (my brother and I) watched the second season with my cousin (the older).

This year, it's a bit weird because I won't have any préesents, only money.

And that's my fault, I didn't have any ideas.

I'll see friends and for the new year, I'll celebrate itcelebrate the new year with friends so it'which will be funny.

This sentence is a little awkward though the grammer is technically correct. Funny does not mean fun, it refers to something humorous.

I will take advantage of the holidays withby just resting sometimes, because I amhave been pretty tired in réecent days.

I think it's the accumulation of pressure with the tests, sports with the gymests and sports.

I deffineitely need a holidays!

What's my plan for the holidays?

In 5 days, I'll be in holidays.the holidays will start

I can't wait for the holidays, school is so boring at the moment!

Happily, I wdon't have almost any tests in the 5 next 5 days.

I only will have a NSI (test on Numeric and Informatic Science) one and a TP (Traveaux pratique in French (pratic work?)) in Chemistry.

Not sure what TP is to correct it

I will go to the south ofern France.

This could be correct if you meant that you are literally going to the south of France (as in Africa or something) but I imagine you meant southern France

Moreover, the first part of the final season of Stranger Things hwas been released last month, so we will canbe able to watch it together.

It reminds me a memoryof the time, maybe 5 years ago, when we (my brother and I) watched the second season with my older cousin (the older).

Many friends have told me that it's really cool, so I am really excited.

I will celebrate Christmass with them.

This year, it's will be a bit weird because I won't have anyill give money instead of préesent, only moneys.

And that'Which is my fault, because I didn't have any gift idea.s

The second week of Christmas, I'll be at home.

I'll see friends and forcelebrate the new year, I'll celebrate it with friends so it' with them which will be funny.

Presumably it will be funny as well but probably meant to say fun :)

I will take advantage ofuse the holidays withto just resting sometimes, because I amhave been pretty tired in récent daysrecently.

I think it's because of the accumulation of pressure with the tests,exams and doing sports withat the gym.

I deffineitely need holidaysa break/rest!

It's not wrong but it is semantically weird

Please tell me how you foundI’d like your opinion on my English!.