All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
We want to point out first that an illegitimate daughter will not bear the consequences committed by those who gave birth to her if she is a believer and does righteous deeds. Allah the Exalted says (what means): {Whoever is guided, is only guided for [the benefit of] his soul. And whoever errs, only errs against it. And no bearer of burdens will bear the burden of another. And never would We punish until We sent a messenger.} [Quran 17: 15]
So, she is mandated, like other people, and addressed by the commands and prohibitions of the Sharee'ah, and whatever is permissible and forbidden to others, the same applies to her. Allah the Exalted says (what means): {Whoever does righteousness, whether male or female, while he is a believer - We will surely cause him to live a good life, and We will surely give them their reward [in the Hereafter] according to the best of what they used to do.} [Quran 16:97] and, {...The most noble of you in the sight of Allah is the most righteous of you. Indeed, Allah is Knowing and Aware.} [Quran 49:13] Ibn Taymiyyah said in Majmoo' Al-Fataawa regarding a person born out of Zina (fornication or adultery): “If he believes in Allah and does righteous deeds, he will be admitted to Paradise; otherwise he will be rewarded or punished for his deeds just like other people, and the reward or punishment is based on deeds, not on lineage.”
Regarding reciting the Qur’an at the funeral, it was reported that some scholars held that it is permissible to recite Qur’an on the deceased. It was also reported that some of the predecessors recommended to recite Qur’an at the grave during the burial. In his book Ar-Rouh, Ibn al-Qayyim mentioned some narrations regarding this, but other scholars prohibited it. Some commentators of Ar-Risalah quoted Malik as disliking it. Based on this, whoever leaves the recitation (does not recite) is on the right path, and whoever recites over the dead, then he follows the example of some predecessors, so there is no harm in it.
If by recitation of Qur’an is meant to present its reward to the dead, then the scholars differed about its ruling. We hold that the preponderant view is that the dead will benefit from this and the reward will reach him. However, it is better to supplicate for the deceased and give charity on his behalf since such deeds are proved by the sound Sunnah and all scholars agree that the reward of supplication and charity will reach the dead.
Allah knows best.