Thanks to the writing practiceompts on LangCorrect, I have become better at translating what I want to say into English.

I you are talking about practicing writing, "writing practice" would not be plural. If you are talking about the prompts/questions available to answer on LangCorrect, you would use "the writing prompts" (as in my correction). If you are talking about just writing journals in general, you could say "writing journals" (plural because you have written more than one).

I have overcomed the fear that I can't make myself understood as expected.

The past participle of "overcome" does not have an "-ed" ending.

"As expected" is not needed on the end -- it is implied.

The most important thing is not to hesitate to ask andquestions or make mistakes.

This sentence does not make it clear what you would be asking. From context, I assume you would be asking questions. You can use "and" or "or," but "or" sounds more natural.

English conversation is too fast for Japanese people to listen to and pronounce correctly.

If you are focusing on hearing something specific, you are "listening to" it. If you are hearing things but not focusing on anything specifically, you are just "listening."

For almost one year, I've taken online English lessons.

This is fine, but "almost a year" would usually be more natural.

Thanks to writing practices on LangCorrect, I am becomeing better at translating what I want to say into English.

We'd normally just say "practice", I think the plural form is quite rare. And you would use present progressive "I am becoming" or present perfect "I have become" here - "I am becoming" stresses that it is an ongoing process, "I have become" stresses recent results.

Simple present "I become" is *okay* here but a native probably wouldn't use it. It would be for, for example, repetitive actions: "every time I practice, I become better". Or to focus on things happening at the same time: "as I practice I become better".

Speaking English as a novice requires quick responses and courage to talk with foreigners as an incompetent speaker.

"incompetent" is too harsh here, it implies... total unsuitability to a job, I suppose. Someone who's simply learning isn't incompetent, unless they are in a role that requires a lot more skill than they have. "Novice" seems good to me.

"Speaking English as a novice" is the subject, "requires" is the verb, "quick responses and courage" is the object. I don't think it's *wrong* that you have "as a novice" split off from the rest of the subject like this, but it's awkward.

I have overcomed the fear that I can't make myself understood as expected.

"overcomed" is not a word - present perfect (which, yes, is the correct tense here!) requires the past participle of overcome, which is "overcome". Usually you would expect past participle to be the same as the simple past, which is what you were trying for with "overcomed", but that's actually "overcame", and "come" is an irregular verb so they aren't the same anyway. Just English things!

It might be more appropriate to fear something in future tense - "the fear that I won't be able to make myself understood". But I'm not sure. What you mean is clear, anyway.

The most important thing is to not to hesitate to ask andquestions or make mistakes.

"not to hesitate" is okay but this is a little more natural, and "ask questions" is more helpful than just ask. Otherwise it's slightly mysterious what you might be asking. At first I thought you were saying you would both ask mistakes and make mistakes - ask mistakes is nonsense so it's easy to figure out what you actually mean, but adding the object makes it even easier.

"and" is also okay but "or" sounds better.

However, response speed and accuracy still remain as my problems.

Same here, "as" is okay but unnecessary and this is more natural.

English conversation is too fast for Japanese people to listen andto or pronounce correctly.

"listen" is intransitive, but there's a clear indirect object here - the Japanese people aren't simply listening, they are listening to English conversation. We can do what you've done here with transitive verbs and direct objects: "English conversation is too fast for Japanese people to understand", that's fine. But with intransitive verbs and indirect objects we need the "to".

"listen" is slightly strange here, "understand" is closer to what I think you mean. But I'm not sure exactly what you mean.

Thanks to writing practices on LangCorrect, I have become better at translating what I want to say into English.

I have overcomed the fear that I can't make myself understood as expected.

The most important thing is not to hesitate to ask for help and make mistakes.

I'm not sure if "for help" correctly conveys what you wanted to say, but you need something after "ask", as you ask for something.

English conversation is too fast for Japanese people to listen to and pronounce correctly.