I believe it's important to learn synonyms of words, as for example if someone uses petite for small you would not understand what this means. However, it's is fine enough to just learn the most commonly used word as you learn English.

Introduction for volunteer(ing) work. I would need some corrections.

Hello. I'm Zsolt from Hungary. I'm traveling around South East Asia in 2019. I try to keep my expenses as low as possible whilist (whilst) I'm traveling. I've (I) worked in Hungary, England and Denmark as a: restaurant manager, waiter, kitchen porter, cook... Also, I can do almost any handwork. I'm looking for volunteer(ing) work in exchange for accomodation(accommodation) and some food. I love animals and nature. Backpacking and traveling around South East Asia (and later around the World) is on my bucket list. Dear Host, I hope you are willing to help me make my dreams come true :)

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Hi Zsolt, just like to let you know that:

volunteer is the noun and Volunteering is the action.

There's no need for I've as worked already means that you been there. 

Abortion.

Nowadays, abortion had become a very common practice. This prompted many hot duscussions(discussions) about imorality(immorality) and it`s legal status. Some people believe that abortion should be forbidden, whereas other(s) hold the opposide (opposite) side. In this essay, I will look analyse the both opinions and present my own.

On the one hand, it is necessary to understand that abortion takes root from (a) lack of sexual education and neglect of contraception. Many teenagers do not understand the consequences of unprotected sex, despite the fact that they know there the kinds come from.(This sentence doesn't make sense) As the (a) result, not the young nor their parents are not ready to raise a child as it requires (them) to give up the study that is necessary for the most well-payed jobs. Consequently, without proper education, the young parents fail to provide for the child. From that perspective, it is quite anderstandavle (understandable) why so many people prefer abortion.

On the other hand, it is not a secret that abortion is a very harmful procedure and may cause many reproduction problems. Moreover, some women may even completelly(completely) lose the reproduction ability. Furthermore, abortion might only take the fetus's life but badly on a person`s future perspectives as a parent. Also, there is a moral aspect of the problem, since many people do not see any difference between murder and abortion. The advocates of that point belive (belief) that abortion should be forbidden on moral grounds and it is easy to understand them.

All in all, this seems to me a very compcicated (complicated) problem. I personally believe, that sometimes abortion could be the only way. But on the other hand, the percentage of fertility disfunction(dysfunction) caused by abortion is very high. The only way that seems right to me is to draw as much attention to the problem as possible and to organize the special classes in schools to put more light on the topic.

Dear members, please tell me

Hello, could you be so kind and tell me, which sentence is correct?
1 I wish you a quick recover
2. I wish you a quick recovery
Thank you so much in advance.

I wish you a quick recovery is correct.

This is is a count noun (recovery) is considered an action recover is just the verb. 

São Silvestre Marathon

Last Monday(December 30), took(taking) place in São Paulo the 94th São Silvestre Marathon, a very popular street race of Brazil. It has become a(an) last year's day (end of year) tradition in Brazil and it's always been largely broadcasted by the local television channels.
An estimated number of 30.000 runners took part in that edition, both in male and female categories, and something interesting to point out is that not every runner is there to reach the podium. Many do it as a personal challenge; then, if they make it through the 15 km race, it is a victory to those people. Moreover, there are those who are there neither to win nor to perform a personal challenge, but just for fun, and because of that it is (a) very common sight, seeing people running, wearing all sort of fancy dresses just to take part in this thing which they consider a big party.
Out of the people who are there to compete in earnest, African runners have always been highlighted. They often reach to the highest places on the podium and this year it wasn't different: both the female and male competitions had its podiums crowded with runners from places such as Ethiopia and Kenya. The best that Brazilians runners achieved was the 8th place, both in the male and the female competitions, which means that it wasn't a good year for the Brazilian runners. Let's hope they can have a better performance next year,

My life

Hi my name is Daniil and I am from Russia. I really like(enjoy) to  study(studying) English. Every day I work on my pronunciation. I read books and listen to songs. Also, I really like to watch videos on different topics. I would like to study abroad in the future.

Perfect, just some few little mistakes with the naturality of your writing. Enjoy sounds more natural and then followed by studying. 

to is a  preposition and connects the activity together. 

g(G)reetings to a potential language partner

Hello, my friend! I read your profile and I think we could do language exchange since I see that you have the Spanish in your list of languages to learn. (is there another way of saying this?)

Hi everything is perfect, there's no need for (the) Spanish by itself is already grammatical. You can also use the Spanish language but this is not normally use in English.