@ziawj2,
The letter in italics; my changes in bold, underlined; explanations, where needed, in plain text:
Dear Mr. and Mrs. Smith:
We have not seen one another [one another or each other--your student was correct; otherwise, the question would be, "seen what?"]
for a long time. I would like to invite you to my house to have dinner at 7 p. m. on May 15 ["am delighted" is rather too effusive for what can be considered a friendly letter]
.
As we are good friends, I know you love fish [it is understood that you refer to what will be eaten]
, so I will cook fish soup. Of course, I will also serve a good wine [you don't prepare the wine, the vintner does that, you just serve it]
. Then we can enjoy the meal and tell funny stories [if you were chatting about funny stories, you would be discussing funny stories rather then telling them to one another]
. There is a shopping mall near my house, perhaps we can go shopping there. after dinner. I think it might be a wonderful night.
Could you drop me a line to let me know whether you can come? I’m looking forward to your reply.
Yours sincerely,
He Ying