Suggested correction, hope that it helps!

Native language

Nowadays, almost all people use computers and the internet. You We type more frequently on the computer more othen than we write by hand use handwritting. I notice that it is not easy to write or read handwritting because of my eyes are get have gotten used to reading typed typewritten text.
Because As a result of using this global network the internet, people are getting lazy: they like to contract words, use slang or even make mistakes on purpose. Sometimes I have to think a lot before being able to write a correct sentence in Russian, and often I can not remember the appropriate rule. ,so Thus, I try to use find another way of writting making my point or even use other words if I'm not sure about the spelling (hopefully fortunately, the Russian language is very rich). I always liked Russian grammar and had a good mark for this subject got very good grades in it. but However, now it is very hard to use proper language because you often frequently see wrong incorrect spelling, grammar and punctuation. I don't tell claim that I am super-russian-speaker a perfect speaker of Russian, but I try do not to forget my mother-language tongue.

It looks like a lot of corrections, but the key point is the following:  this was very easy to understand and the corrections are mostly small details to help you achieve a more polished, natural sounding English.  Really nice work, I'd say!

Native language

Nowadays, almost all people use the computer and the Internet. You type on the computer more often than you use handwriting. I notice that it is not easy to read or write handwriting because our eyes get used to reading typed text.
Because people use this global network(which global network?), they are getting lazy. They like to contract words, use slang, or make mistakes on purpose. Sometimes, I have to think a lot before writing a correct sentence in Russian and often, I can not remember the rule, so I try to use another way of writing or use other words if I'm not sure about spelling. (hopefully Russian language is rich){What do you mean in the parentheses?} I always liked Russian grammar and had a good mark/grade(U.S.) for this subject but now it is very hard to use proper language because you often see the wrong spelling, grammar and punctuation. I don't say that I am super Russian speaker but I do try to not forget my mother language.

Native language

Nowadays, almost all people use a/the computer and the Internet. (Лучше сказать "almost everyone uses a computer and the internet)

You type on the computer more othen quickly/efficiently than use handwritting you can write by hand.

I've noticed that it is not easy to write or read handwritting because of my/your eyes are get have gotten used to reading typed text.

Because of using this global network people are getting lazy; they like to contract words, use slang or make mistakes on porpose purpose.

Sometimes I think a lot before to write writing a correct sentence in Russian and I often can not (can't!) remember the rules, so I try to use another way of writting or use other words if I'm not sure about the spelling (hopefully Russian language is rich).

I always liked Russian grammar and had a good marks for this subject, but now it is very hard to use proper language because you often see wrong spelling, grammar and punctuation. I don't tell say that I am a superior Russian speaker, but I try do not to forget my mother-language.

Молодец, Леночка ) Давай на WhatsApp практикуем на английском языке )

Native language

Nowadays almost all people use a computer and the Internet. You type on the computer more often than you use handwriting. I notice that it is not easy to write or read handwritting because my eyes have gotten used to reading typed text.
Because of using this global network people are getting lazy: they like to contract words, use slang or make mistakes on purpose. Sometimes I think a lot before writing a correct sentence in Russian and often I can not remember a rule,so I try to use another way of writing or use other words if I'm not sure about the spelling (hopefully the Russian language is rich). I always liked Russian grammar and had a good mark for this subject but now it is very hard to use proper language because you often see wrong spelling, grammar and punctuation. I don't say that I am super russian-speaker but I do try not to forget my mother-language.