I’d like to study Chinese a little, because I want to go on a trip to Taiwan.

Little (spelling)

I try to write while using google translate a lot, because my Chinese level is underbelow the beginner. level.

I want to go to Hsinchu city.

And I want to eat some delicious fried rice vermicelli.

Couldan you tell me if you know any good restaurant?s?

Do you know any good restaurants (sounds more natural)

I’d like to study Chinese a little, because I want to go on a trip to Taiwan.

I try to write whileby using google translate a lot, because my Chinese level is under beginner.very low.

Could you tell me if you know any good restaurants in Taiwan?

I’d like want to study some Chinese a litle, because I want to go on a trip to Taiwan.

"I'd like to" -> "I want": optional
If you want to avoid saying the same "want" twice, you can change the "I want" in "because ..." to "I'd like".

"study Chinese a little" -> "study some Chinese": was correct but now is more natural
Note that now, "some" modifies "Chinese" whereas before "a little" modifies "study".

I try towrite write while using gh the help of Google tTranslate a lot, because my Chinese level is under beginnerI'm new to Chinese.

"I try to write while using google translate a lot" -> "I write with the help of Google Translate": was correct but now is more natural
Note that I have removed the 多用 meaning, but if you want to include it you can say "I write while making frequent use of Google Translate".

"because my Chinese level is under beginner" -> "because I'm new to Chinese": was correct but now is more natural

Could you tell meLet me know if you know a good restaurant?!

"Could you tell me if you know" -> "Let me know if you know": was correct but now is more natural

"good restaurant" -> "a good restaurant": was incorrect, is now correct

I’d like to study Chinese a litla little bit of Chinese, because I want to go on a trip to Taiwan.

Spelling error

I try to write while using gneed to use Google tTranslate a lot, because my Chinese level is under beginner.that of a beginner (alternatively, "my Chinese knowledge is very basic")

Beginner would be the lowest level of understanding in the first place. I understand what you mean though- that you don't know a lot of Chinese.

Could you tell me if you know of any good restaurants? / Could you recommend me some good restaurants?

I’d like to study Chinese a little, because I want to go on a trip to Taiwan.

I try to write while using google translate a lot, because my Chinese level is under beginner.

This is technically correct, but this isn`t a phrase that anyone would say in English. A more natural way to say this would be:

I write while using google translate a lot, because my level of Chinese is very poor.

Could you tell me if you know a good restaurant?

In this case, English speakers wouldn`t usually say Could you. Something like this would be more natural:

Do you you know any good restaurants?