A 680 score is within the range of top programs. You should only retake the test if you have the time to dedicate to preparation, you have not taken it more than 2x, and you really think you can score 700+.

In answer to your second question - a resounding YES - average essays will hurt your application. High GPA and GMAT scores are not differentiators for top programs. Essays are the only way in which applicants can communicate their unique traits, knowledge of a particular MBA program, and why the program will specifically help them to achieve their post-MBA goals. If you submit generic essays then you are wasting your time and money.

Does having the test for three times have a negative effect on admissions?

A 680 GMAT is within the range for top schools, but not exceptional. I would be more worried about your lower quant score. Some schools feel that anyone below 50%ile will have trouble handling the coursework. Your 54%ile is perilously close to that level. IF you believe you can raise your quantitative score you should consider retaking the test.

As for essays. They are CRUCIAL! Weak essays will kill your application. Top schools have many times as many people with outstanding GPAs and GMATs as they can accept. Essays give them a picture of you as a person. The business school experience is so strongly affected by the personalities and interactions of the students, that essays are weighted more heavily for b-school than for other professional schools.

As a Kaplan consultant, I have seen people with killer essays and great interviewing skills and recommendations be accepted to schools with GMAT score 100-150 points below the average.