My first language is Russian and I speak've spoken it all my life.

However, being a Kazakh ethnically, I also should know the Kazakh language as well.

Unfortunately, I know it worse than I know English.,

I, at least in terms of vocabulary and expressing myself.

I felt the best option would be to join these two sentences. As others have stated, this sentence in its current form isn't a complete thought. If you join the sentence with the previous, then it should be fine

I can understand when someone speaks it, but it's hard for me to actually speak it.

I've started fromby learning basic words, and I was surprised by how many simple words I actually didn't know.

I don't believe your original sentence was incorrect, but in my opinion it sounds more natural this way

In Kazakh, I barely know a half of those words.

I also have to learn itEnglish for my master's degree.

I hope being inside the environment ofmmersed in the language helps me to improve faster.

Again, what you said was fine, but in my opinion my correction expresses the same sentiment in a more natural way.

My first language is Russian and I speakhave spoken it all my life.

However, being a Kazakh ethnically, I also should know the Kazakh language as well.

I'm not positive on the phrase "being a Kazakh"

With certain cultures it can be seen as slightly insensitive to include the a. For example, "being a chinese" can be seenas offensive by some people. This definitely is not seen universally though.

It's definitely safer to not include the a.

Unfortunately, I know it worse than I know English in terms of vocabulary and expressing myself.

In terms of vocabulary and expressing myself.

This is not an independant sentence

I've started fromby learning basic words, and I was surprised how many simple words I actually didn't know.

There isI have a list of 625 basic words, and when I look through it in English, I found out that I didn't know only 10-15 words from it.

There -> I have:
There implies a level fo familiarity. For example, if this list is famous then it would be appropriate to use there in this circumstance.

In Kazakh, I barely know a half of those words.

Half is a weird word in that you don't include a before it.

For example, the following are all correct:

I have an apple
I have half of an apple
I have half an apple
I have an eighth of an apple.

It's kind of weird to learn one of your native languages as if it wasere a foreign language.

The were/was in this situation is challenging but I would probably go for were.

I hope being inside the environment of the language helps me to improve faster.

What you have is gramattically fine. Can I suggest that:

I hope being inside the environment of the language helps me to improve faster.

My first language is Russian and I speakhave spoken it all my life.

The present perfect is needed because you're describing something that continues from the past.

However, being a Kazakh ethnically, I also should know the Kazakh language as well.

Unfortunately, I know it worse than I know English, in terms of vocabulary and expressing myself.

In terms of vocabulary and expressing myself.

This looks like it was cut off from the previous sentence.

I can understand when someone speaks it, but it's hard for me to actually speak it myself.

It's fine without "myself," but it sounds more complete this way, and there is also more emphasis on the contrast.

I've started fromby learning basic words, and I was surprised how many simple words I actually didn't know.

"From" doesn't sound egregiously wrong to me, but "by" seems better.

There is a list of 625 basic words, and when I looked through it in English, I found out that I didn't know only 10-15 words from it.

In Kazakh, I barely know a half of those words.

It's kind of weird to learn one of your native languages as if it wasere a foreign language.

I hope being inside thean environment ofwhere the language is used helps me to improve faster.

This was fine, but this sounds more idiomatic to me. You could also use "a Kazakh-speaking environment."