I don't need a certificate to study abroad or get a job, but I still I want to know what level I am now.

Sounds more natural like this. Could also add in “level of language proficiency” to specify what type of level it is, and it might sound a bit better to say “I am at now.”

Writing would be difficult for me, because I reliedy on the dictionary and the internet to correct my words and grammar, and/so without them I would write the broken sentences in the exam.

Present tense for “relied” would be better here (relied —> rely). You would use “relied” if you had said what you relied on the dictionary and internet for. For example “because I relied on the dictionary and the internet to write these sentences”
It sounds better/more natural if you use a word like “and” or “so”, or you could also start a new sentence.
The main case where you would say “the broken sentence” is if you were talking about a broken sentence. For example “the broken sentence was a result of not using the dictionary and internet.” In this case it indicates that you have also talked about a broken sentence previously.
After removing “the” in “the broken sentence” it isn’t grammatically correct so you could replace the with a (“a broken sentence”) or make sentence plural (“broken sentences”) depending on if you would be writing multiple sentences or only one.

And about Swith speaking, I watched a video of the IELTS speaking test, where the examiner asked the student what she thought about environmental issues, and she answered with insightful opinions in fluent English.

It sounds a bit more natural like this.

If a stranger were to ask me the same question in Mandarin and asked me to respond immediately, I would be too nervous and (I would) screwed up.

With “ask me” you could say “were to ask me”, “asked me” or “asks me”.
With “asked me” and “asks me”, you would change the second “ask me” to the same thing.
“Screwed” (past tense) can’t really be used to refer to a hypothetical situation unless you were to say “I would have screwed up”

I don't need a certificate to study abroad or get a job, but still I want to know what level I am nowmy written English is at.

Could be a bit confusing for people who don't know what the IELTS test is. Therefore, I would recommend explaining what you are improving at.

Writing would be difficult for me, because I reliedy on the dictionary, and the internet to correct my words and grammar, without them, I would write the brokenwrong/badly worded/bad sentences in the exam.

I assume you are writing more than one sentence in the exam. Broken works but isn't very accurate, I would recommend using more accurate words which describe your sentences better.

And about SpeakingNow I will speak about the verbal part of the exam, I watched a video of the IELTS speaking test, the examiner asked the student what she thought about environmental issues, and she answered with insightful opinions in fluent English.

Your first 3 words are weirdly structured. Try to avoid using and as a sentence starter.

I think my problem may not only be my English.

You don't need to add my, but I feel it makes it easier to understand.

If a stranger asks me the same question in Mandarin, and ask mI have to respond immediately, I would be too nervous, and screwed up my answer.

I am thinking about taking the IELTS test at the end of thise year.

Both "this" and "the" are correct! I think it is more natural to say "the" (most people would assume you mean 2024)

I don't need a certificate to study abroad or get a job, but still I want to know what level I am now.

Writing would be difficult for me, because I reliedy on the dictionary and the internet to correct my words and grammar, w. Without them, I would write the broken sentence is on the exam.

And about Speaking, Is for speaking, I (recently) watched a video of the IELTS speaking test, t. The examiner asked the student what she thought about environmental issues, and she answered with insightful opinions in fluent English.

If a stranger asked me the same question in Mandarin and ask me to respond immediatelyexpected an immediate response, I would be too nervous and screwedmess up.

If I want to take the IELTS test, I will need to deliberatethoroughly practice the test procedures.

I don't need a certificate to study abroad or get a job, but still I want to know what level I am now.

Or "what level I am at now"

WThe writing part would be difficult for me, because I reliedy on the dictionary and the internet to correct my words and grammar, w. Without them, I would write the broken sentences in the exam.

And about SRegarding the speaking part, I watched a video of the IELTS speaking test, t. The examiner asked the student what she thought about environmental issues, and she answered with insightful opinions in fluent English.

If a stranger ask me the same question in Mandarin and ask me to respond immediately, I would be too nervous and screwed up.