Three years ago i stopped, I left my professional carreer because iI needed to take care ofor my children. Three years ago, I left my professional career because I needed to take care of my children.

We tend to use the term "leave" when ending a job. You can say "to take care of" or "to care for"

Three years ago i stopped, I quit my professional carreer because iI needed to take care ofor my children. Three years ago, I quit my professional career because I needed to take care of my children.

1. When talking about leaving a job, the verb “quit” is most commonly used 2. Whenever you use the word “I” in English, it must be capitalized 3. In English, the phrase is normally said as “take care of ___” There’s also a few spelling errors here

Now iI want to improve my eEnglish so that iI can apply for (a job / work) again. Now I want to improve my English so that I can apply for (a job / work) again.

"English" and "I" are always capitalized. "Apply for a job" highlights one singular job, like perhaps you have a specific position in mind, such as with your last employer. But if you want to speak generally about many jobs, "apply for work" is slightly more general

Now iI want to improve my eEnglish so that iI can apply for a job again. Now I want to improve my English so that I can apply for a job again.

The word “English” is a proper noun and must be capitalized

I hope that in one month iI wouldill be able to speak and whrite much better than iI do now. I hope that in one month I will be able to speak and write much better than I do now.

We are talking about one month in the future, and not a hypothetical scenario, so "will" not "would"

I hope that in one month iI wouldill be able to speak and whrite much better than iI do now. I hope that in one month I will be able to speak and write much better than I do now.

1. You should use “will” here instead of “would” since you’re talking about the future 2. The word “white” refers to a color. I think you mean the word “write”

HI hope iI can (do it). I hope I can (do it).

I that Hope iI can. I that Hope I can.

This phrase works in informal conversations when it’s already been established that the subject is you, but in this case, you should include the subject, that being you

Why lLearning English aAgain mMatters to mMe Why Learning English Again Matters to Me

Title capitalization rules