I have already written three diary entries here, but I noticed I haven't introduced myself, so let me do, a little later thoughhere I go.

Very US alternative.

Here are more:

I've already written three diary entries here, but I just noticed that I haven't introduced myself so please let me do so now.
I've already written three diary entries here, but I just noticed that I haven't introduced myself so please allow me to do so now.

I belonged to a Chinese economic seminar and half of the members were Chinese.

We need to use the plural form of "member" here.

For the time being, I'm gonnaing to work for a company and acquire expertise for at least for three years, and, after that, I want to go to Australia on a working holiday.

As the previous person said, "gonna" is very colloquial. We don't really use it in writing unless we're making up a story.

So I started to learn English in earnest and, by the time I will go, I want to speak English more fluently.

"by the time I go" is a subjunctive phrase so "will" isn't used. 楽しそうです。頑張ってください！

My hobbies are reading books, cooking, listening to music, going to concerts ( unfortunately, I can't it right now in this situation. ), drinking with my friends.

or

My hobbies are reading books, cooking, listening to music, going to concerts (unfortunately, I can't go right now in this situation), drinking with my friends.

And what I want to do the bemost after this situation is TRAVELING.

or

And what I want to do the most after this situation is *travel.*

All capitalization (all caps) can be considered rude when writing so we try to use italics (斜体) instead. If we can't use italics, we use asterisks (*) or underscores (_).

はい、私も旅行したいです！

I have never been to Hawaii so I'll definitely I will gogo there.

US alternative

or

I've never been to Hawaii so I'll definitely go there first.

I have already written three diaries here, but I noticed I haven't introduced myself, so l. Let me do, a little later though so even though it's late.

"so let me do, a little later though."

"A little later though"

I am assuming you want to say 少し遅いけど、やて見て you want to say this then "even though it's late" is more fitting.

"So let me do" → it feels awkward to use this here, either you'll go with
1) "Let me do so" やて見て
2) "Let me try" 試して

"So" → usually you would use it in the middle of sentence/casual

For the time being, I'm gonnaing to work for a company and acquire expertise at least for three years, and after that, I want to go to Australia onfor a working holiday.

gonna → we only use it when we speak/casual texting; formal/writing should be "going to"

Going to vs Will

Will → usually is still a plan
Going to → Plan has been created & is in progress

So I started toHence, I am learning English in earnest andly so by the time I will go, I want toill speak English more fluently.

Other words than "So" → only for beginning sentence
- Hence
- Therefore
- That's why (Casual)

"I started to learn English in earnest and by the time I will go"
本気に英語を勉強して初めています → you are still learning english right now it's considered as present continuous

And what I want to do the best after this situation is TRAVELINGtraveling.

I have never been to Hawaii so I will definitely I will gogo there one day.