A letter to friend with information, that one of your relatives is traveling to his/her country

Hi, everyone, I tried to do both tasks in 1 hour and so if you dont mind, please help to review both in this thread. If possible, please estimate the score for me.

Task 1:
Write a letter to your friend to inform him/her that one of your relatives is traveling to his/her country and say
- Describe the relative
- Why is he/she traveling there?
- Why do you think they should meet?

Dear Jimmy,

It has been a long time we met since my graduation trip in 2009. I am really appreciated for your accommodation offer to my cousin, Jerry who is recently graduated from Bachelor of Music in the University of ABC. This is his long-waiting trip to Europe. You can imagine how excited he is now. He is so surprised that you offer him to live in your house in Vienna during 3rd March to 30th March. I hope he will not cause any trouble to you. If he does, please tell me and I will punch him after he arrives home.

I believe you are the most suitable person to show him around Vienna where has numerous of theatre and shows as you are such a world-class opera singer today. With your experience and network, I truly believe you will give him the valuable advice about this field.

Besides, are you sure you do not want him to pay you the rent? My auntie said you have to come to visit us once you are able to do so. She promised to serve you the world best dinner for your kindness and help. I have to go now. Thanks for taking care of my cousin.

See you soon.

Cheers,
Tom

Dear Yon Choy,

I revise some words in the first paragraph. I think the revised one is more readable. You can take up my suggestions if you think they are helpful to your writing.

It has been a long time since our last meet in 2009we met since my graduation trip in 2009 . I am really appreciated it that you would like to offer a roomfor your accommodation offer to my cousin, Jerry, who is recently graduated from SchoolBachelor of Music atin the University of ABC. This is his first long-term waiting traveltrip to Europe.

He is so surprised that you allowoffer him to live in your house in Vienna fromduring 3rd March to 30th March.
... I will punch him whenafter he arrives home.

Many thanks for your help.

I will keep your comments in my minds so as to write a better letter for ielts