Is it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?

It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).

What should a praying person who doubts having offered one, or two prostrations in the third Rakah (unit of prayer) do?

Whoever has doubts about their prayer should consider what is less i.e. the above person should offer another Sajda (prostration) and complete his/her prayer, then offer Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.

What is the ruling on combining prayers at the Musala (Place for prayer) of a shopping center because of heavy rain, knowing that some people come from outside that center?

Praise be to Allah, the Lord of the Worlds.

If there is hardship in going back to that Musala at the time of Asr or Isha` prayers, then it is permissible to combine prayers in twos only (Duhr with Asr and Maghrib with Isha`). Kindly consider calling us. And Allah Knows Best.

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.