Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
I work for a company whose manager refuses to allow employees to leave during work hours. Do I incur sin if I secretly went out to join the congregation at the Masjid? Is doing so considered a breach of trust?
Praise be to the Lord of the Worlds.
We recommend that you pray at work to encourage your colleagues to follow suit, because whoever guides to good has the like of the reward of the person who actually does it. And Allah The Almighty Knows Best.
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).
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.