Hi, I'm a 20-years-old Japanese university student, and I'm aiming to study abroad in Taxeexas, USA to learn the latest in Engineering.

By "study the latest Engineering", do you want to study in Texas because you think it's a cutting-edge engineering program? If so, I would say "learn the latest in Engineering."

However, I'm actually not good at English that. I currently have only 90 score in donly have a score of 90 on the Duolingo test and 500 score inof 500 on the TOEFL itpITP.

Saying "score of" before a number score on a specific test is optional, but if you do want to include it, it's better to say "score of" before the number.

These tests' limited time is so hard for me, and I especially inhave low proficiency in the writing and speaking sections, I have low proficiency, making my entire score spoiled.

Your original sentence isn't wrong, but it feels a little more natural to structure it this way to me.

I'll post an essay-style writing written on time pressure and a diary or a murmur sometimes.

Hi, I'm a 20-years-old Japanese university student, and I'm aiming. I intend to study abroad in Taxeexas, USA to learn the latest Engineering.

Mostly good, with a few typos. I've just rephrased to make it sound more natural.

However, I'm actually not that good at English that I currently haveas I only 90 score in dd 90 on the Duolingo test and 500 score inon the TOEFL itp.

"That I currently have" doesn't quite work here. "As" makes more sense to connect your initial statement ("I'm not good at English") with the justification ("I only scored X on the tests").

I've rephrased the sentence so that it's more active rather than passive.

These tests' limited time is so hard for me, and especially in writing and speaking sections, I have low proficiency, mak time limit on these tests are a challenge for me, the writing and speaking sections especially. In these sections I score low, ruining my entirwhole score spoiledoverall.

"challenge" makes more sense than "hard" in this context.

"I have low proficiency" sounds a bit odd here, as nobody really says that in English. Same with "making my score spoiled". One says "X spoiled Y", not "X made Y spoiled."

I'llHere, I'll sometimes post an essay-style writingpassage written onunder time pressure and. Or a diary or a murmur sometimes-entry. Or just a whinge.

"an" because "essay" begins with a vowel sound, namely "EH".
"passage" is a thing you post whereas "writing" is more of an activity.
Not certain what you meant by "murmur" but it doesn't quite work. I am guessing you meant "complain" or "whinge".
I've separated each piece of writing into different sentences just to make the difference between them clear. (I'm assuming you don't write the diary under time pressure, but maybe I'm wrong.) You don't have to do this.

Hi, I'm a 20-years-old Japanese university student, and I'm aiming to study abroad in Taxeexas, USA to learn the latest Engineering.

Usually the 's' in years stays when you say something like "I'm 20 years old," but the 's' gets dropped when you say "a 20-year-old".

However, I'm not actually not good at English that. I currently have only 90 scoreonly have a score of 90 in dDuolingo test, and 500a score of 500 in TOEFL itp.

The word ordering for adjectives (形容詞) are reversed in English compared to Japanese. e.g. 「持ているだけ」is "only have".

These tests' limited time is so hard for me, and especially in writing and speaking sections, I have low proficiency, makspoiling my entire score spoiled.

tests' is both plural and possessive (meaning that there are multiple tests you are talking about. If you meant to only talk about 1 test, then it would be "test's"). "making my entire score spoiled" and "spoiling my entire score" both sound kind of weird in English (though "spoiling my entire score" sounds slightly better). A more natural way to say it would be "making my score worse" (or, if you're talking about multiple tests, "making my scores worse").

I'll post an essay-style writing, written onwith a time pressure and, on a diary or a murmur sometimes.

"written with a time pressure" is a slightly separate thought (an "aside") from the rest of the sentence "I'll post an essay-style writing on a diary or a murmur sometimes." So it should be wrapped in commas (,).

I hope I'llto continue to doing this for a long time.

The "I'll" is a little redundant. Also, "to doing" never sounds correct in English, it would have to be "to do," so another way to write this sentence could be.
"I hope I'll continue to do this for a long time"