Please check my article .

I have to write a letter to my friends parents.
So I need someone's check.

Hello. I'm ⚪︎⚪︎.
How is it going?
Thank you for inviting me for lunch. together.
I really had a great time with you. there was There were many things which are were first time experiences for me in Taiwan.
I do appreciate you guys' and ⚪︎⚪︎'s support.
I would like to say thank you very much to you guys and ⚪︎⚪︎ also.
And thank you for your gift for my family. My family was glad to recieve your gift. They are thankful rejoice and be happy.  
They also say thank you very much to you guys.
I had stayed in Taiwan for just one week. however, Even in this short time, I came to like Taiwan much more than before.
If I had have time, I would want like to go again.
I really hope to see you again. I would like for you to come to Japan.
Thank you for everything . My first trip in Taiwan is provided unforgettable memories for me.

Note: "you guys" is a regional phrase. In the US southern states, we say "you all" or "y'all". Officially, the plural of you is the same, you. It's all understood. I'd recommend you use whatever form your host family used.