Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Is it permissible for a Muslim woman to wear trousers at home?
Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. And Allah Knows Best.
A man cursed Allah, is he allowed to perform prayer without making Ghusl?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Cursing Allah is an act of apostasy and one who commits it must utter the testimonies of faith, make repentance, take back wife; however, it isn`t conditioned that he makes Ghusl (Full body ritual purification) to pray. And Allah The Almighty 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.