In Taiwanparticular, I want to go to Hsinchu city. In particular, I want to go to Hsinchu city.

Your original sentence is grammatically correct, but I think it sounds more natural this way.

In Taiwan, I want to go to Hsinchu city. In Taiwan, I want to go to Hsinchu city.

Hsinchu city is famous for producing bifun, or rice noodles, so I want to go there and eat some fried bifun. Hsinchu city is famous for producing bifun, or rice noodles, so I want to go there and eat some fried bifun.

Hsinchu city is famous for producing bifun, (aka rice noodles, so I want to go there and eat some fried bifun. Hsinchu city is famous for producing bifun, (aka rice noodles so I want to go there and eat some fried bifun.

Not a correction, but 米粉 in Japanese is like just one kind of 粉 so this may be confusing depending on who you're talking to. Food words get really messy but in English we'd say "rice noodles" or specifically the Japanese 米粉 is usually just "rice vermicelli" but this will mean something different to someone speaking Chinese.

Hsinchu city is famous for producing bifun, rice noodles, sowhich is why I want to go there and eat some fried bifuno Hsinchu. Hsinchu city is famous for producing bifun, rice noodles, which is why I want to go to Hsinchu.

I like to eat fried bifun, so I want to compare tohe original bifun and the oneto that which I geat in Japan. I like to eat fried bifun, so I want to compare the original bifun to that which I get in Japan.

I like to eat fried bifun, so I want to compare tohe original bifun andto the one which eat in Japan. I like to eat fried bifun, so I want to compare the original bifun to the one in Japan.

I like to eat fried bifun, so I want to compare to original bifun and the one which eatauthentic bifun to what we have in Japan. I like fried bifun, so I want to compare to authentic bifun to what we have in Japan.

This sentence is fine but you can get it a little bit clearer by removing redundancy if you want. There was nothing wrong with it though. For food, we tend to use "authentic" in this context. "The one" sounds a little specific if you're not talking about a specific shop.

I like to eat fried bifun, so I want to compare to original bifun and the one which eat in Japan. I like to eat fried bifun, so I want to compare original bifun and the one in Japan.

I’m home alone now, because my parents went to travelling to Taiwan. I’m home alone now, because my parents went travelling to Taiwan.

or "... because my parents went to Taiwan on vacation."

I’m home alone now, because my parents went to travel to Taiwan. I’m home alone now, because my parents went to Taiwan.

The "travel to" is a little unnatural.

I’m home alone now, because my parents went toare travel toing in Taiwan. I’m home alone because my parents are traveling in Taiwan.

Small thing, not that important.

I’m home alone now, because my parents went to travel to Taiwan. I’m home alone now, because my parents went to Taiwan.

OR "my parents travelled to Taiwan"

I want to go to Taiwan alstoo. I want to go to Taiwan too.

I want to go to Taiwan alstoo. I want to go to Taiwan too.

Hard to explain but "too" sounds slightly more natural at the end of sentences like this.

I want to go to Taiwan alstoo. I want to go to Taiwan too.