Ok...So, as these are interview questions and you might be using them, I have corrected your entry much more "harshly" than I normally would.  I made it sound as professional and natural as I can.  A lot of the "corrections" aren't really corrections, they are just stylistic choices that make it sound better in an application. So don't think you made a lot of errors :P.

Give an example of a time when you were leading and influencing the direction of a project or task. 
I was a the vice president of the swimming club during my college days. Once I held an annual party for over 300 alumni and the number of alumni was more than 300. I set created a system for  the way to contacting with them, I fixed with a call quota for each member of the club and I made a detailed manual (script) for a phone calling to make help our members feel easy to more comfortable making a the calls. As a the leader, I took care the responsibility for of the most greatest number of calls. With these Using the methods I laid out, we achieved the goal on time. 

2. Describe a situation when you faced a difficult problem and how you were able to solve it. 
Once I had to arrange an interview for our clients (musicians) with a radio program and the radio producer wanted our clients to perform at on his program. However, our clients didn’t want to perform until they could be sure about knew the condition of the musical instruments at the radio station. However, it was impossible for my clients to check the condition in person them personally because they were foreigners and living outside of Korea. 

To solve this problem, I decided to go went to the radio station by myself. With the help of the radio producer, I took various pictures of the instruments and filmed them to record their sound as well. I sent the pictures and video to my clients by email. As a result, I could get received their confirmation and so I made it to met both sides’ expectations. 

3. Describe a time when you were able to come up with a new idea that became key to the success of some activity or project. 
One day, my boss at the my previous job asked me to come up with an idea about for new business items to sell in other countries. Hence, I researched a trend in the music industry of Korea and I found out an attractive item. At that time, an animation production studio made an animation with some classical music pieces and they then threw a live concert with it. It was getting popular in Korea. I thought it could be popular in other countries as well so I made a proposal to analyze the animation-concert’s potential overseas and suggested making a partnership with the animation company and getting a the rights to sell the animation concert overseas. My boss was satisfied with my work and actually our company decided to represented the animation studio later. We sold the item to an orchestra in China.

Notes: 

"a vice president" means there are multiple vice presidents.

"easy" is not used as a feeling.  You could use "at ease" if you wanted.

you perform "on" a program.

Good work.  If you have any questions please let me know.