Fantastic job, Cho! Here are my (very small) corrections:

#1 - wedding ceremony
I cannot go to the wedding ceremony because I have plans with my friends. So I will ask my friend to pass the money to the groom as a wedding gift on behalf of me.

Great use of future tense (I will ask my friend)! I change "I had plans" to "I have plans" because the plans are still in place so you should use the present tense in this case.

#2 - sprain
I sprained my back a few months ago. Although my back is nearly recovered, I'm still reluctant to play basketball.

The recovery process for injuries is ongoing so we typically use the present tense to discuss the current state of an injury.

#3 - visit to China
I'm planning to go to China this summer with my girlfriend. We have been together for more than 3 and a half years, but it will be my first visit to China. I'm looking forward to seeing her family and her hometown.

Perfect! Excellent grammar!

#4 - tragic accident
There was a tragic accident that happened in Korea a few days ago.

(Or: "A tragic accident happened in Korea a few days ago." If you use "there was" you need "that" between "accident and "happened" because "was" is the verb, but if you remove "there was" then "happened" becomes the verb.)

A person was attempting to commit suicide and jumped from the 21st floor of a building, but unfortunately he fell on a passerby and they were both dead at the same time.

You used perfect grammar! That is an Incredibly sad story.