Is the marriage that took place after the husband entered upon his wife before the marriage contract invalid? And are the children in this case illegitimate? And what is the ruling on marriage in general if one of the spouses is not observant of prayer at the time of the marriage contract?

If a husband has intercourse with his wife before the legal marriage contract (aqd), he has committed a reprehensible act (munkar), and the wife should refuse. However, repentance erases what came before it. The marriage (nikah) is valid according to many scholars, even if she married before repenting. The wife's negligence in prayer does not invalidate the marriage, because the majority of scholars hold that one who abandons prayer due to laziness does not commit disbelief that expels him from the fold of Islam. Therefore, your marriage is valid, so live with your husband in kindness and do not pay attention to whispers (waswas).