I have been travelling the world for two years.

Slight spelling mistake on traveling. When you are describing a duration, you want to add “for” before the duration to connect it. Example: “I have been waiting for 30 minutes.”

I have been to many European countries.

The correct adjective for something that is in Europe is, European.

But I want to learn new cultures and see new places.

Cultures should be plural here, since you are describing more than just 1.

Many European countries were similar to each other.

There were old buildings, grey clouds, silencet streets.

The correct past tense for the adjective “silence,” is silent.

I decided to make money to discovery Asia.

Discovery is a noun, you want a verb here to describe you doing it. Discover would be correct.

That is exciteding.

Since it is exciting right now, you want the word exciting. Excited would imply you were excited in the past but not currently. Example: “I was excited.”

I hope to have fun on my new travels.

I’m not exactly sure what was meant to be here, but it’s not a complete sentence. Something that would fit would be something like “I hope to have fun on my new travels.” It is missing a subject. We know you are hoping, but what are you hoping for?

There were different cultures, foods, nice beaches, and beautiful natural places.

Since there are multiple cultures, make sure to add an “s” to the end to make it plural. The plural spelling for “beach” is “beaches.” When describing 3 or more things separated by commas, make sure you add “and” to the last thing you are talking about.

I think many Asian people are friendshiply and cheerful.

The adjective for someone from Asia is Asian. The adjective for someone who is nice and might be your friend is “friendly.”

Asian countries are cheaper than European countries.

So many tourists coame in recent years.

The past tense for “come,” is came. You could also correct the sentence by saying “so many tourists have come in recent years,” because adding have turns come in to present tense.

It means you don’t carehave to care about your bags, when you swim or walk.

While you could technically say “you don’t care about your bags, when you swim or walk.” This makes it flow better.

Singapore, Thailand, Vietnam, Cambodia, Indonesia, Philippines, Japan, and South Korea… C are calling to me :). I will come , see itsee them soon.

You could technically use an ellipses here, they are used when you have a sentence that will be expanded on in the next sentence. But combining it with your next sentence makes it a more complete thought. Since you are talking about multiple countries you want to see, “them” is used instead of “it” here.