Welcome Mary Glad you decided to post... I hope you don't mind, but I fixed your text a bit. I didn't try to change it too much or rephrase it in anyway, just fixed what I found egregiously wrong. Good job overall.

My name is Mary.
My native language is Russian. I want to know English better, that's why I'm here. I like English very much and I hope that the information and the interaction with the people of this forum can help me.
About myself.
I'm 24 years old, I was born in Moscow.
I play the piano, I've been studying in a music sсhool since the age of 6. I like music very much.
Last year I've got a diploma of higher education and my profession is economist and computer science.
I like reading, arabic dancing, theatre and animals(I have two dogs and a cat).
I have favourite singer - Sarah Brightman.
That's all for the first time. Sorry if I made any mistakes in my text--my English is not that good