First notebook entry: Introducing myself

I am learning english language, because I want to freely communicate when ride for a border. ( I don't think you mean that u go across to the border on a horse, I assume u meant travelling)
My native language is russian, and I grew up in Ukrainia.

nice try 

First notebook entry: Introducing myself

I am learning english language,in order to  communicate when ride for a border.
My native language is russian, and I grew up in Ukrainian.

I am learning English (the English language) as I would like to communicate freely/speak (the language) fluently when I travel abroad.

I am studying English/looking to improve my English so that I can communicate freely when travelling abroad.

(I can imagine that you translated ‘ride for the border’ literally from Russian ехать, ездить (travel путешествовать ) but ‘ride’ is used mainly re bicycles, horses etc., and occasionally for vehicles e.g., ride on a train. If you mean перейти границу then cross the border but I think you mean ‘abroad’ за границу as in ‘to travel abroad’ — путешествовать за границей.

First notebook entry: Introducing myself

I am learning English languages(or "I am learning the English language."), because I want freely to communicate when while having a  ride for a around the border freely. (or: I want to communicate freely with others when I ride to the border)
My native languages is Russian, and I grew grow up in Ukrainian.

Comment:

Here is something I want to remind you:

1. the words for a language or a nation needs to be written as “Russian”(begin with a capital letter)

2.when th e noun. in the sentence is singular, you don't need to add "s" at the end of it. such as "My native language is Russian".