Text 1: Thanks to the revolution, eachany person of any nation has the right to be President.

You seem to be referring to a specific revolution, in which case the article "the" would be expected. If you're referring to multiple revolutions, you can write "Thanks to revolutions".

But in the Ottoman era, only the sultans's son wascould be the successor whoand nobody knew whether he iwas skilled or smart enough to be Head of Country.

(1) You're referring to the Ottoman era, which is something specific, so the article "the" is expected.
(2) "Sultans" should be singular ("sultan"), because "son" is singular as well, unless all sultans had the same son. If you want to keep "sultan" plural, you'd write "only the sultans' sons". Note that for plural nouns ending with "s", we only write the apostrophe. Note also that "sons" is plural.
(3) The second half of your sentence is quite awkward and difficult to read. Simple replacing "who" with "and" immediately solves this problem.
(4) It should be "was" and not "is", because you're referring to something that happened in the past.
(5) I think it'd be more natural to write "skilled or smart enough", implying that there's some baseline requirement.

That's why we are appreciated Mustafa Kemal Ataturk tofor bring Ring republicanism to our country.

(1) "Are" and "appreciated" are incompatible, because they are in different tenses. If you want to write in the present tense, you can just write "appreciate".
(2) The phrase is "appreciate (someone) for (doing something)".
(3) republicanism: support for a republican system of government.

Now we can elect who gets 50%+1 as President.

I'm not sure what "50%+1" means. Perhaps you can explain it to me?

(In) This way, Turkey's people improve themselfves.

"Themself" is not a word, because "them" implies the plural, while "self" implies the singular. The word is "themselves".

Text 2: Erdoğan is afraid of losing to Imamoğlu to lose next election.

The phrase is "lose to (someone)".

He won four elections over Erdoğan.

Therefore, a made-up accusations were createdmade in order to avoidprevent Imamoğlu to runfrom running for president.

(1) "A" and "accusations" are not compatible: "a" is singular, while "accusations" is plural.
(2) The phrase is "make accusations (against someone)".
(3) prevent: keep (something) from happening.

Every court session, they suggests baseless evidences for blaming him.

(1) It should be "suggest" and not "suggests", since "they" is plural.
(2) "Evidence" is an uncountable noun.

Demostration is a constitutional right.

Text 1: Thanks to revolution, eachvery person of any nation has the right to be the President.

But in the Ottoman era, only sultans's son was the successor who nobody knew whether he iwas skilled or smart to be the Head of Country.

That's why we are appreciated that Mustafa Kemal Ataturk to bringbrought Republic to our country.

(In) This way, Turkey's peoplecitizens improve themselfves.

Text 2: Erdoğan is afraid of Imamoğlu to loslosing the next election to Imamoğlu.

He won four elections over Erdoğan.

Therefore, a made-up accusations were created in order to avoid Imamoğlu to run for president.

Every court session, they suggests baseless evidences for blaming him.