If the prayer has been commenced and someone is performing Tahiyyat al-Masjid (greeting of the mosque prayer) in the first rak'ah, should he exit his prayer with taslim (salutation) or without taslim? And where should one look during bowing (ruku')? And what are the reasons for heedlessness regarding contemplation of the Hereafter?

If the prayer has been commenced (iqamah has been called), then there is no prayer except the obligatory one. This includes not starting a prayer when the iqamah is called, and interrupting a prayer if one had started it before the iqamah, so that the worshipper can catch the virtue of the opening takbeer (takbeerat al-ihram). This is supported by the Prophet’s (peace be upon him) pulling of Ibn Abbas and saying, "Are you praying four rak'ahs for Fajr?" when he was praying while the mu'adhdhin was calling the iqamah for prayer. And whoever interrupts a supererogatory prayer to join the congregation, may exit by saying salam or by an act that nullifies the prayer.