Is it permissible to listen to the Holy Qur’an at work while some employees are talking about worldly matters and not listening, and is it obligatory to listen to the Qur’an without speaking?

It is prescribed to listen attentively when the Qur'an is recited, and one should not be preoccupied with talking or other things, because the listener of the Qur'an is receiving an address from Allah Almighty.