All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First of all, all perfect praise be to Allaah, Who guided you to Islam and we ask Him to make you firm and steadfast on His Religion until the day you meet Him.
As regards your questions, we have already issued Fatwa 84923 clarifying the ruling of affiliating with groups which organize Da'wah activities provided they adhere to the methodology of Ahlus-Sunnah Wal-Jamaa'ah, and we clarified thereof that the difference in some views among the different organizations should not hinder participating in the good and righteousness which those organizations carry out, so please refer to the above-referred Fatwa.
For more benefit on how to organize the administration of Da'wah organizations and charities in the west, please refer to Fatwa 88689.
In these two Fataawa, you will find many answers to your questions.
With regard to the remaining questions, it should be noted that the mosque has many roles in addition to its fundamental role, which is performing the prayers and reciting the Quran and the legislated mention of Allaah. The mosque used to be a refuge for some Muslims who did not find a shelter, and it was a place for welcoming the delegations who came to the Prophet . He used to invite them, teach them and guide them therein. The mosque was also the spot to run Islamic politics. It was a place for consultation and it had other numerous functions.
Therefore, it is permissible for any Muslim group to hold study circles and programmes in the mosque if it is for the purpose of serving the religion. However, the permission of the Imaam or the person in charge of the mosque should be sought. Not seeking their permission could lead to anarchy or to using the mosque in things which it should not be used for.
With regard to your question whether or not ''the members of the Muslim community (if there are as many as like 10 or 20) have a right to request a new Imam or a new sister to lead the mosque", the answer is that the Muslims in any country in the world should stay in coherence and cooperation instead of disputing, arguing and quarrelling, as this will decrease their role and weaken their strength. Allaah Says (what means): {…and do not dispute and [thus] lose courage and [then] your strength would depart.}[Quran 8:46].
Finally, it should be noted that it is permissible for the Imaams of the mosque to ascertain the identity of any person who wants to organize activities in the mosque, however, they should not prevent him if they are sure that he does not want any evil or harm.
Concerning your participation in the administration of the mosque, please refer to Fatwa 89181.
To conclude, we ask Allaah to increase your religious knowledge and make you steadfast.
Allaah Knows best.