All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
Deliberately throwing the Quran on the floor out of disrespect constitutes an act of disbelief. However, if he threw it on the floor without intending any disrespect, then it does not count as an act of disbelief and the doer is excused if he did so while being unaware of what he was doing. Please refer to fatwa 133314.
Assuming that he did throw it out of disrespect and that such an act is considered an act of disbelief on his part, if he repents to Allaah of such a sin before the woman’s ʻiddah (post-divorce waiting period) expires, then he can take her back in marriage with no need for a new marriage contract. Please refer to fataawa 106948 and 99158. about the ruling on the marriage when one of the spouses apostatizes.
We would like to point out the gravity of anger and the evil consequences that it may incur. Therefore, the Sunnah of the Prophet abounds in warnings against anger and its grave effects. Abu Hurayrah narrated that a man said to the Prophet "Give me advice," so he said several times, "Do not become angry." [Al-Bukhari] Ibn Rajab wrote, "It is deduced from this hadeeth that anger is the source of all evils and that avoiding it is the path to attaining all that which is good." For more benefit, please refer to fatwa 86681.
Neglecting the prayer is a grave matter, to the extent that some scholars declared the person who neglects it a disbeliever even if he does so out of laziness. The majority of the Muslim scholars, though, held that the person who gives up the prayer out of laziness is not declared a disbeliever. In any case, such a sinner should be advised about the gravity and evil consequences of abandoning prayer. If he repented to Allaah, then this is the desired objective; otherwise, it is recommended to leave him. The Hanbali scholar Al-Buhooti wrote, "If a husband neglects the right of Allaah, then the wife is like him in this regard (i.e. resorting to divorce), so it is recommended for her to seek a khulʻ (divorce at the instance of the wife in return of compensation payable by her) from him due to him neglecting the rights of Allaah."
However, if the wife chose to be patient and retain her marriage to that man while advising him to give this sin up, then there is no harm in that.
Finally, if the husband’s family praised their son by saying that he observed the prayer, yet when he married it turned out to be untrue, then they have committed a misdeed and fell short in offering honest advice in this regard. However, this does not affect the validity of the marriage contract.
Allaah knows best.