I'll be glad to help with proofreading. Let's take a look:
"Since the twentieth century, the divorce rate has begun to rise dramatically, in many countries."
You don't need the comma.
"While years ago, divorcing was a rare fact in societies, today it is quite common due to various factors."
How about: "While years ago divorce was rare in certain societies, several factors make it quite common today."
"Turkey is one of the countries, in which divorce rate has been following an upward trend since 2001."
Again, you don't need the comma, but you do need to insert "the" in front of "divorce."
"The first cause for the rising divorce rate in Turkey, is the women's changing role in the society."
No comma here, either. :-) Also, take out "the" before "women's." (You would need it for the singular "woman's", but not the plural "women's." I know, I know--English is weird!) Also, delete "the" in front of "society."
"After the reforms held by Ataturk, women have begun to play a more significant role in life."
I would begin the sentence, "Since the reforms introduced by Ataturk, women . . . " Looking ahead, I see that you are using the past tense in the next sentences, so you need to make it match here: ". . . women had begun . . . "
"They had the opportunity to acquire an education, instead of sitting at home looking after their children, they started working."
Delete the comma after "education", but leave the next one and insert "and" after it.
"Before, it was difficult for women to end their unhappy marriages, however after the developments mentioned above women had the opportunity to divorce, and to live the life they desire."
I recommend changing the comma after "marriages" to a semi-colon and deleting "however." You also need to change "desire" to "desired", since you are writing in the past tense. The sentence would flow better if you said "after Ataturk's reforms" rather than "after the developments mentioned above."
"Accordingly, the divorce rate is on increase since these improvements."
Insert "the" before "increase." Also, the sentence implies that the rising divorce rates are an improvement (it doesn't actually say
that, but it does imply
it); maybe you could use "changes" instead of "improvements."
"Another cause of the rising divorce rate is rising infidelity."
It's usually best not to use the same descriptive word twice in one sentence (unless you're doing it for effect). I suggest saying "growing divorce rate" and "rising infidelity", but it's up to you.
"Due to the lack of passion and excitement in their relationships, or because of the fear of getting older many spouses have an affair."
Insert a comma after "older."
"All these factors culminates in adultery."
It should be "culminate" rather than "culminates."
"The final but the most important causes for the rising divorce rate in Turkey are economic crises and financial problems."
Begin the sentence, "The final, most important . . . "
"According to Turkish Statistical Institute's (TURKSTAT) statistics, divorce rate has gained momentum since the 2001 economic crisis."
Insert "the" before "divorce rate."
"Because of the 2001 economic crisis many people lost their jobs and the cost of living increased dramatically."
I recommend rewriting this: "Many people lost their jobs during this time, and the cost . . . "
"The struggle to make a living gave damaged marriages."
"Furthermore, in 21st century, people don't have the nerve to endure financial difficulties; therefore, instead of struggling together, they prefered to struggle alone, and got divorced."
Insert "the" before "21st." "Prefered" needs to be "preferred." And you can delete "therefore." When you use a semi-colon, it tells the reader that the two halves of the sentence are related in some way (in your case, cause and effect), so you don't need to use "therefore" or "however" or any other word that you would use in a separate sentence to indicate a relationship. Oh, and one more thing: you start the sentence in the present tense, then switch to the past. It would be best in this case to say "prefer" and "get."
"Today, many people think that it is easier to live alone due to financial reasons, and the upward trend of divorcing still continues."
"Divorcing" is OK, but "divorce" is more idiomatic.
Sometimes I wonder how people ever managed to invent a language as complicated as English. As I believe I told you before, your English is really quite good. It takes years of reading, writing and practice to learn all the little tricks, and you are well on your way!
Keep up the good work, and best of luck to you!