: Writing as a non-native speaker English is not my first language, but as an English student, I'd always like to write in that language... I have many story ideas but my skills are not that

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Start writing short stories instead of a novel. While it is a different focus of skills, short story writing will let you develop your use of English very quickly. By working with online or local critique groups, you'll likely get great feedback on your use of the language.
Writing groups, and mostly critiquing others work, will be tremendous help in improving your skills. If you live near a large city, then you'll likely find a bunch of writing groups advertising for writers online on social media and sites like meetup. You can also find them through local libraries and writing communities. There are also a whole bunch online -- some a general like scribophile.com and others are specialized like critters.org (fantasy/sci-fi)
Obviously reading, general fiction in the language you want to better understand is important. I knew a Swedish researcher who came to the US not speaking a word of English and when I met him four years later, you'd never now he wasn't a native speaker. He said he read Louis Lamour Westerns to learn colloquial English.
And, you can certainly have non-native English speaking characters in your stories. Having a non-native speaker as narrator might be something you want to avoid since your desire is to improve your spelling, grammar, and though you didn't say it, I imagine idiom and phrasing as well since English has UK, American, and Indian dialects but that depends on your target audience.
Spell Checkers will help will help, but Grammar checkers like the one built into MS Word, or add ons like Ginger or Grammarly are fraught with errors. All are right most of the time, but are wrong often enough to provide confusing feedback when learning English grammar, particularly with the complex sentence structures used in creative writing.

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Maybe you can write a story narrated from first person perspective from someone like yourself, a non-native English speaker. That way any grammatical and/or spelling errors will only make the story more authentic.

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