I recommend the stylistic changes shown in blue.

My name is Nastya. I have been studying English for several years, but I still want to improve. I would be happy to help you practice your Russian.i!!! Hi!!! Hi!!! Hi!!!

"I am happy" would be more appropriate if you were already helping the person.  Example:  Chat partner:  "Nastya, thank you for helping me with Russian, but I think I am taking too much of your time."  Nastya:  "Don't worry about it.  I am happy to help you practice your Russian."  

My name is Nastya. I have been studying English for several years, but I still want to improve.I am happy to help you practice your Russian.