I’m saving up forto livinge in Australia because I lost my past job as waitress due to the corona virus and moved to the country side to get farm job, but I’ve been'm still waiting for starting yemy job to start.

From a writing perspective, "I'm saving up to live in Australia" doesn't quite connect with the rest of the sentence. I've fixed what I perceive to be the grammar mistakes though.

After my visa is expiringes this November, I’m going to NY to learn how to sell Japanese products in the mostis challenging situation.

"Is expiring" suggests something ongoing, but your statement clearly refers to after that event has finished.

I want to support Japanese companies and promote their products and services to the world.

Japan has many good quality products, but many people who is self-employed people or SME havs are in trouble because they’ are lucking ofunable to find people whto take over their business and skills.

"Luck out" has a positive connotation, so it doesn't really work here.

Also, as domestic market is getting decreasedeclining more and more, especially in the traditional products industry, so they have to expand their market to the world.

However, there arhave only been a few people who can do it so far, due to their English skills and marketing skills required.

You're describing a state that continues from the past to now ("so far"), so the present perfect is better.

That’s why I came to Australia to study English/ and marketing things, and somehow I have to survive in here.

Since before, when I joined my ex-company, I’d wanted to live in abroad, so I’d been saving up for it.

I'm not sure if this fits your intended meaning, but this is one way to make the sentence grammatical. Otherwise, there is a run-on sentence.

Thanks to that, I managed to come here eventually, but also I thought if I could save money more, I cit would be easier to live in here.

I’ve been thinking about how I can save money forsince then, just in case since thenI need it.

I’m saving up for my living costs in Australia because I lost my past job as a waitress due to the corona virus and. As a result, I moved to the country side to get a farm job, but I’ve been waiting for starting yet.the job to start.

I separated the two sentences since the original sentence was a run-off sentence.
Make sure you add articles (the and a/an) before nouns. Here is when to use articles:
https://owl.purdue.edu/owl/general_writing/grammar/using_articles.html

After my visa is expiringes this November, I’m going to NY to learn how to sell Japanese product in the mosts, as the industry is facing a challenging situation.

I changed "in the most challenging situation" to "as the industry is facing a challenging situation", because I read below that it's getting more difficult for Japanese companies to sell their products. It sounds better that way.

I want to support Japanese companies by promoteing their products and services to the world.

Japan has many good quality products, but many people who isare self-employed or SME have in troubledifficulties because they’re luacking of people whto take over their business and skills.

people is plural, so you need to say "are" instead of "is"

Also as the domestic market is getting decreaseing more and more, especially the traditional products industry, they have to expand their market to the world.

However, there are only a few people who can do ithis so far, due to their English skills and marketing skills.

You can combine "English skills" and "marketing skills" to become "English and marketing skills" to sound smoother. You can do this with anything similar, for example:
Instead of saying:
"I am buying red apples and green apples."
I would say:
"I am buying red and green apples."

That’s whye reason I came to Australia was to study English/ and marketing things, and somehow I have to survive in here.

Since before, I joined my ex-company, I’d wanted to live in abroad, so I’d been saving up for it.

Thanks to that, I managed to come here eventuallyI managed to eventually come here thanks to saving up, but also I thought if I could save money more, Ire money, it could be easier to live in here.

"in here" sounds like you are inside somewhere (like a house). For this scenario, just say "here"

I didn't know what you meant by "that", so I put "thanks to saving up", but maybe you also meant thanks to your ex-company. When it's unclear what you are talking about (like when you talk about a few different things beforehand), mention the actual thing instead of saying "that", "this", "thing", etc

Since then, I’ve been thinking about how I can save money for just in case since then.