I am not interested in taking the TOEIC exam, which is not related to my job at present, but I may take it in before long for somone reason or another.

The phrase "for some reason" means the same as "a reason I don't know". For example, "For some reason, John left the window open and now the room is really cold." This is the same as saying "I don't know why John left the window open. It was a bad idea!"
So, in your example, it sounds like you're saying "I may take the exam, but I don't know why I would do that." It sounds like you're going to take it, even if you think it's a bad idea. I'm not sure this is the meaning you wanted.
The phrase "for one reason or another" might be better here.

A couple of years ago, I’ve taken took a look at a textbook of the TOEIC at a bookshop, and when I saw the price of the textbook, I realised it was so expensive that I couldn’t afford to buy such an expensive oneit.

For finished times in the past, use the past simple. "A couple of years ago" is a finished time (it does not continue until now), so you need to use "took" (the past simple form).
For unfinished time (time periods that continue until the present moment), use the present perfect tense, "I've taken".
If you don't use the phrase "A couple of years ago", it is fine to use "I've taken" (the present perfect), as you are talking about an experience in your life. Your 'life' is a time period which continues until now, and therefore is 'unfinished time'.
If you'd like more help, feel free to message me, or take a look at this link:
https://www.perfect-english-grammar.com/present-perfect-or-past-simple.html

I gave up buying the one.

"I gave up buying one" - "one" = TOEIC textbooks in general; any TOEIC textbooks.
"I gave up buying it" - "it" = that one particular textbook you mentioned in the previous sentence (the one which was too expensive).
These are two different meanings. Please choose the sentence which makes more sense to you.

As I am not satisfied with the status quo, to overturn that reality, I came up with an idea for the textbook.

Just checking - "the textbook" means that one particular textbook you were looking at in the shop. Only one.
If you mean 'all TOEIC textbooks in general', you should write "I came up with an idea for TOEIC textbooks".

It wais not so phenomenal.

You are talking about "as of now", which is in the present. So make sure to use the present tense "is" here as well.

It wais not so much of a big deal, either.

Or, "It is not a big deal, either".
Either is fine, but I think the first version sounds better here.

The other day, I asked my Chinese friend to buy the textbooks of TOEICsome TOEIC textbooks in China.

"textbooks of TOEIC" makes sense and the grammar is fine, but it sounds a bit unnatural.

As a result, she somehow or other found a new version of a TOEIC textbooks which wereas composed of three textbooks.

You are talking about one book, so make sure to use the singular "was".

It was only 52 Chinese yuan, which is equivalent to about 1000 Yyen.

Currency written like this does not need a capital letter.

It is veryso affordable, even I can afford to buy such reasonable textbooks.

Or, "It is very affordable, so even I can afford to buy such reasonable textbooks."
But I think the first version sounds better here ("It is so...")

I wanted to buy the textbook that came with a CD.

But no matter how hard she tried to find it, there wereas no such a textbook on the internet, so it cannoouldn't be helped.

We ended up downloading all sources of thearing part listening files from the publishing company's site.

Actually, she is the one who downloaded them all and sent me them by E-mail.

There were eight parts of the hearing ability, and I heardlistening files, and I decided to listen to one of them still midway.

"to listen" is an active action. You make the decision to listen to something.
If you "hear" something, you don't have a choice - it is a passive action. Here is an example of this difference:
1) "The radio was on when I got home, and I heard some nice piano music." (I had no choice - the radio was already on and the sound entered my ears.)
2) "I wanted to listen to some music, so I turned on the radio." (I made the decision to actively listen to the music.)

When I hearAfter I listened to it for a while, I was so shocked.

It should be realised it was to lasting for 45 minutes.

I only listened to five questions from the beginning, but I felt the speed of the questioning voices wereas way too sluggish and easy.

"the speed" is singular, so use "was".

ThaIt was so laughable.

We're talking about the whole situation in general, so we can use "it". It just sounds a bit more natural.

I had thought the hearlistening parts werould be very difficult to comprehend.

We can use the past perfect tense ("had thought") for one past event which happens before another. This makes it clearer that originally, you had thought they were difficult. But then, afterwards, you realised they weren't.
"Would be" is the past tense form of "will be". So, it's like saying you thought "I think the listening will be very difficult", and putting all of that into past tense.

On the contrary, I could make it through them, and could makeget nearly full marks.

With that said, I might be pushing my luck too far.

Nice phrase! But make sure to use the continuous "(I might) be pushing" if you are talking about the present, and use the present perfect "(I might) have pushed" if the action was in the past.

It is the right time now for me to snap of my daydream, isn't it?

I haven't gotten the three textbooks yet, but they wouldI might get theme a month later.

I'm not sure about what you mean here, so I've corrected it to what I think you want to say.
If this is wrong, please let me know and we can try and make a better sentence together.