Please check:

I believe the essential qualities a leader must possess are to set a vision and to be able to lead. A leader must be able to set a vision to seek for improvement. Seeking for improvement helps make the idea grow better and better. A leader must be able to lead in order for his/her group to agree and the group's goal. Being able to lead means to inspire others to do so as well.

With the verb "seek" you don't need to use "for" -- delete that word wherever it appears after "seek."

I believe the essential qualities a leader must possess are to set a vision and to be able to lead. A leader must be able to set a vision to seek for improvement. Seeking for improvement helps make the idea grow better and better.
There's still too much repetition in here. How can you combine the ideas and get rid of repeated words? This should be distilled down to ONE sentence.

This is good: Being able to lead means to inspire others to do so as well.
"to do so" should be made more detailed, though.

Keep revising! It's getting better!!

You need to understand we really don't know what makes a leader. I grow girls into being leaders in girl scouts, and I can assure you, there is not a single model to do that. However, I do follow Robert Greenleaf's model of a leader: one who enables others by serving their needs so they can accomplish goals. You would be wise to review Greenleaf's model to get some perspective on different leadership models. Greenleaf's model works wonders for girls...teaching them the value of community service, organizing, planning, taking action, and making the world a better place. http://en.wikipedia.org/wiki/Robert_K._Greenleaf

Another perspective...

http://www.salesgrowthspecialists.com/blog/tag/robert-k-greenleaf/

To check whether the qualities you listed are essential for a leader, we can evaluate them based on common understanding and research on leadership. Here's how you can assess these qualities:

1. Setting a vision: A leader's ability to set a vision is indeed a crucial quality. A clear and inspiring vision helps team members understand the direction they are heading and provides motivation. To check the importance of this quality, you can research successful leaders and their approaches to establishing a vision. Look for examples of how the vision has influenced their team's performance.

2. Seeking improvement: Seeking continuous improvement is a valuable trait for a leader. This quality implies that the leader is open to change and progress, creating a culture of learning within the team. To verify the importance of this quality, you can explore leadership theories or real-life examples that emphasize the significance of growth and improvement in leadership.

3. Leading and inspiring others: The ability to lead and inspire others is considered fundamental for a leader. A leader should be able to guide the team towards a shared goal, motivate members to take action, and maintain a positive work environment. To validate the significance of this quality, you can study leadership styles and practices that focus on influencing and inspiring others. Examine case studies or examples of leaders who have successfully motivated their teams to achieve great results.

By conducting further research on these qualities, you can gather evidence and insights to support or challenge your belief about the essential qualities of a leader. Remember that leadership is a complex concept with various perspectives, so there may be additional qualities to consider as well.