1-In my high school we have an Islamic organization. But, we are having problems with setting up a commitee. What I would like to know is how can we select a new committee in the correct islamic manner?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
The choice of leaders and representatives should be based on the competence of the persons to carry out such responsibilities assigned to him by the group.
This requires the following conditions:
1. The person should be known for his good manners and character. He should be a good follower of the Sunnah, far from innovations and bad character.
2. He should be known for his honesty, assiduity and hard work. Allah Says (interpretation of meaning): {And said one of them (the two women): "O my father! Hire him! Verily, the best of men for you to hire is the strong, the trustworthy.} [28: 26]
3. He should be among the best as far as knowledge is concerned and should be accepted by people. This will help him carry out his activities without much difficulty. This is the case if the choice is done through appointment as Abu Bakr did when he appointed Omar Ibn Al Khattab. But if it is done through elections, the conditions set earlier should be considered before accepting the candidates as Omar did when he chose six and left the final choice of the Caliph to Muslims. Finally, we advise the members of this committee to help one another in doing good in order to serve their brothers.
Allah Says (interpretation of meaning): {Help you one another in Al­Birr and At­Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allâh. Verily, Allâh is Severe in punishment}[5:2] and He Says: {And obey Allâh and His Messenger, and do not dispute (with one another) lest you lose courage and your strength depart, and be patient. Surely, Allâh is with those who are As-Sâbirin (the patient ones, etc.).}[8: 46]
The aims of all activities should be clear. Spreading the religious and educational awareness, trying to unite the hearts of students using all kinds of permitted means of entertainment and providing an Islamic environment for them should be among the aims.
Keeping strictly to the mentioned aims is the responsibility of all members. Every member should set a good example of those aims.

Allah knows best.