Hello, Vitas. This is an excellent entry. The main (but minor - that is, they do <em>not</em> make the text unclear) errors are in 'article' use. I am <em>very</em> glad that I am not a student of English, because articles must be a complete nuisance! Persevere, and they will become clear! 

About one of my hobbies

I and photography

Photography and me / Me and my photography

One of my favorite hobbies is photography. The words ‘photography’ consists of two Greek words: ‘photos’ – which means ‘light’ and ‘graphos’ – which means ‘to write’. Photography allows us to make plane images[множ.] of pieces of the natural world.

Имел ли ты ввиду с "plane", что-то вроде "two-dimentional/flat"? В этом случае было бы хорошое слово.
The first photographic image in the world was obtained by French scientist Nisephore Niepsce in 1822. It was the / a [к сожалению, здесь может быть либо из артиклей!] view from the window in your his room. The exposure was very long. The или His photosensitive material was exposed for a whole day / was exposed all day. Some years later, in 1839, French artist Luis Dager gotobtained an image on a copper plate coated with silver. He opened a portrait studio and made many of the same (kind of/type of) images, which were named daguerreotypes.

Approximately, at this time British researcher, John Talbot researcher has invented a method for producing images using positive and negative.

At approximately this / the same time, British researcher, John Talbot, invented a method for/of procuding images using positive and negative charge.

This method, with some changes and improvement/s, existed for /was used for more than 150 years until the appearance of digital photography.
I started to engage in photography many years ago. When I was 9, my parents presented me with my first film camera and other equipment for film photography ["...presented me with..." or "Gave me ... as a present"]. Now I use digital cameras / a digital camera too, but I still like to make film photography: preparing solutions, developing film and printing paper photography in my dark room.
A few years ago, I studied photography at Moscow State University of design and technology. My teachers there were such famous Masters such as Leonid Kurskiy and Vladimir Vyatkin.

Kurskiy also was also a professor in/at the faculty of operators (not sure here - the faculty of camera operators?) in the main USSR institute of cinema - All-Union State Institute of Cinematography.

('<em>Kurskiy was also a professor in the faculty of operators at the main cinema institute of the USSR - the All-Union State Institute of Cinematography</em>.')

Vladimir Vyatkin is a famous Russian photojournalist who won 1st prize and some 2nd and 3rd prizes at World Press Photo Competitions. He taught students to work at documental photography genre. in the documentary photography genre.

Also I (/I also) studied at the Moscow School of Contemporary Photography from masters who shoot for such magazines as Officiel Russia, Interview Russia, Vogue Russia and others.
My favorite photography genre is portrait photography. I prefer to work in photo studios where I can control the light. I like to make/take psychological portraits and I very much like (/'really like to...'  'particularly like to...'  'like to ... a lot') to work with models - make model tests (there is a better term for this, but I've forgotten it!), fashion and beauty photography.
But from time to time I take my cameras and walk on the city streets or parks. And I like to travel with my camera to other countries.
Some of my works participate in international photography exhibitions and festivals.

Generally, <em>people</em> "participate". So, I suggest something like:

"Some of my works are/have been included in international photography exhibitions and festivals." or, "I have participated in international photograhy exhibition and festivals <em>with my work</em>"


P.S. On/About the picture - the first photography in the world which was obtained in 1882.

It's fascinating, Vitas. I'd love to be able to use a dark room. How long does it take to develop photographs from film yourself?