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 who was on travel prayed Duhr as four Rakhas upon leaving Tafilah heading to Amman. However, on his way to Amman, he prayed Asir as two Rakhas (Shortened). Is what he did correct from an Islamic perspective?
All perfect praise be to Allah, The Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
What he did is correct; he is liable for nothing before Allah The Almighty, since combining and shortening prayers during travel are two separate concessions. Therefore, it is permissible for a traveler to shorten prayer without combining it with another. And Allah The Almighty Knows Best.
I am an employee at Social Security, and I have heard that working with them is forbidden (haram) because they impose an interest rate of 2% on companies and individuals who are late in making payments. Is my job with them haram or questionable?
Please clarify the type of work. If it does not involve the usury (Riba) mentioned, we hope that there is no issue with it, as most of their funds are acquired in a lawful (Complies with the teachings of Sharia) manner. And Allah, The Almighty, Knows Best.
Is it permissible for a woman to wear underwear while performing Umrah?
Yes, it is permissible for a woman to wear underwear while performing Umrah. This is because she should keep her regular clothes that cover all her body while being in a state of Ihram (ritual consecration) for Hajj, or Umrah. However, she should uncover her face and hands, but it is permissible for her to let her head-covering garment drape from her head down over her face when non-Mahram (i.e., marriageable) men pass by her. And Allah Knows Best.