What is the ruling on a man leading his sisters in obligatory prayer, or Taraweeh prayer (Night prayer in Ramadan)?

The prayer of the man who leads his wife, or sisters in prayer is valid, but it is more rewarding for him to offer obligatory prayer in the mosque. And Allah Knows Best.

Is it permissible for a menopausal woman who has blood discharges to fast?

If she reached the age of menopause, and her menses stopped, but later she saw blood discharges that lasted a complete day and night (24) hours, then it is menstrual blood. Still, if these blood discharges lasted less than a complete day and night (24) hours, then it is not menstrual blood, but it is bleeding outside the monthly period (Istihadah), and it does not prevent her from prayer and fast, but she has to make ablution for every prayer.

What is the ruling on loudly sending prayers on the Prophet (PBUH ) after the call for prayer Athaan?

All perfect praise be to Allah, The Lord of The Worlds                                                                                                                                                            Sending prayers on the Prophet after Athaan is a Sunnah for the Mou`zen (caller for prayer ) and the hearer. However, there is no harm in doing it loudly after the end of Athaan, but sometimes, it shouldn`t so that people wouldn`t think that it is an integral part of the Athaan. And Allah Knows Best.

Is it permissible to go to the bathroom wearing a necklace that has the word "Allah" inscribed on it?

All Perfect Praie be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Anything that contains words pertaining to Allah, The Almighty, is desired to be left outside when going to the bathroom, or to be hidden for fear of losing it. And Allah Knows Best.