(X)I would like to be corrected my English if there are some mistakes.

(O)I would appreciate it if you could correct any mistakes I make.

*Grammar note: In Japanese, you use 「。。添削されてほしい。。」right? And when you translate it into English, you would use the passive voice (i.e 'to be corrected' instead of 'to correct'). But in English, we never use the passive voice when referring to someone else's actions.

Next, I would like to write about what happened today.
It was hard, because there are many accidents. -> A lot of things happened today.
This morning, I went to language school which is in the city by bus.
I took the wrong bus, so I didn't arrive at school on time. (You can also say 'to get to school on time')
I was upset and rushed to my class, but there were only a few students and a teacher. (were* = past tense)
Many students are lose, so it was ok to be late. (What do you mean by lose?)
Anyway, being late is not good for my studying, so I should be careful next time.

When the lesson starts, I found my Japanese classmate is a little bit bad.
She was late, too, but she didn't come to the table where I sit.
She didn't talk with me, because I am a Japanese.
I don't feel sad, but I want to speak better than her. (What do you mean by 'better than her'?)
The class was difficult and hard for me, but I have to study by myself.

That's why I am so tired, but I have a nice time with my host family.
An ice cream they served to me was really yummy!! -> They let me have some ice cream which was really yummy!
It was sold at Gelato Messina.
I won't forget the name of the ice cream shop until I visit.

That's all for today. Good night.

Your English is very good! I tried my best to correct your entry in as much detail as I could. If you have trouble understanding any of the corrections I made above, just let me know.

How is your experience studying in Australia so far? I actually live in Sydney, so if you have any questions about things to do, and sights to see etc. feel free to ask!

Good luck with your studies!

My first diary on italki.

Hi! I decided to study writing my diary on italki.
It's my first day to write, so I would like to introduce myself.
I am Elly from Japan.
I live in Australia, and studying English to become an English teacher in Japan.
I like traveling, listening to music, playing sports, and taking spa.
I would like to know if there are any mistakes in my English. if there are some mistakes.
Please do not hesitate to comment on my notebook!

Next, I would like to write about happenings of today with me. today's life.
It was hard, because there are were many accidents.
This morning, I went to language school which is in a city by bus.
I took a wrong bus, so I can't arrive at school on time.
I was upset and ran into my class, but there are a were few students and a teacher.
Many students are lose, so it was ok to be late.
Anyway, being late is not good for my studying, so I should be careful.

When the lesson started, I found my Japanese classmate is was a little bit bad.
She was too late, too, but she didn't come to a the table I sitsat.
She didn't talk with me, because eventhough I am a was Japanese.
I don't feel sad, but I want to speak better than her.
The class was difficult and hard for me, but I have to study by myself.

That's why I am so tired, but I have a nice time with my host family.
An ice cream they served to me was really yummy!!
It was sold at Gelato Messina.
I won't forget the name of the ice cream shop until I visit.

That's all for today. Good night.