Hello Milaniyamiila and welcome to Writefix!

Your essay is very interesting. The examples seem real to the reader, and good stories are far more important than minor grammar or vocabulary errors.  You have avoided the danger of over-exaggeration.

Clive at http://www.englishforums.com/English/PleaseEssayAboutPovertyThank-All/qpnhr/post.htm and some commentators in a forum at http://otvet.mail.ru/question/68300102/ have already given some very good feedback.

I would agree with grouping sentences together and having fewer paragraphs: An introduction, one about your relative in New Zealand, one about your friend in Russia, and a conclusion. 

I feel that although you blame corruption in the introduction and conclusion, you haven't explained the link between corruption and poverty clearly enough. Of course, there isn't time, even in a 383-word essay, to do this properly.

Some vocab issues:

 the country, of which she even had no citizen but only the permission for residence, supported her 

I would change to:

the country supported her, even though she was not a citizen and had only a residence permit.   OR

Even though not a citizen, she was supported by the country until she was able to....    

Sentence length:

I recommend an average number of 12 words per sentence. This sentence has 44 words

To sum up, I want to underline that only developed countries with healthy economy and highly developed democratic values do utmost to support people when they go through difficult time in their lives and in this way they struggle with poverty in their societies.

Try to keep sentences short: 12 words is a good average. Here are three of your sentences:

• Let's compare New Zealand and a former Soviet Republic. (9 words approx)
• She and her children hardly manage to survive. (8 words)
• After emigration 10 years ago she could not find a job because of [her] poor knowledge of the English language. (20 words).

The average is 12.3 - Perfect! It's not a scientific number, but people get lost in long sentences. Pronoun references become unclear. Punctuation becomes more difficult, and ideas harder to untangle, develop and absorb. 

To sum up, I want to underline that only developed countries with healthy economy economies and highly developed democratic values do [their] utmost to support people when they [Who does  "they" refer to?" Countries? People?] go through difficult times in their lives and in this way they [again, who does  "they" refer to?" Countries? People?] struggle with poverty in their societies.

This might change to 

To sum up, only developed countries with healthy economies and strong democratic values genuinely support people in difficult times by helping them to get back on their feet. Corrupt countries, on the other hand, ignore the poor, or force them to pay for ever-worsening services. This results in a downward spiral of poverty which threatens all but an elite.