I. 1. event

   2. available

   3. turned down

   4. going

   5. surprised

II. 1. calendar

    2. so that

    3. preparation

    4. without

    5. hang out

    6. accepted

III. 1. Can

     2. I’m afraid not

     3. might have to

     4. I’d love to

IV. One possible version:

Hi! Harry,

Thanks a lot for your invitation. I’m sorry I can’t go to London to visit you. I’m really busy in the coming winter vacation. First, I want to do something interesting. I’m going to practice English, read classics, improve my handwriting and take guitar lessons. Besides, I want to do more exercise, such as running, playing basketball and badminton. And I’m going to help my parents do some housework. I will make the bed, clean the room, wash the dishes and make some delicious food for them. At the end of the vacation, I will go on a two-day trip with my parents. We are going to Hangzhou by car. If you are free, you can go with us.

I hope we can have a meaningful vacation. 

Yours, 

Li Lei