She became Muslim after having an illegitimate pregnancy aborted; will Allah forgive her and will she meet her child in Paradise?

Firstly: 

Zina (fornication or adultery) is forbidden and is a crime according to all divinely revealed laws. It is abhorrent and is rejected by anyone with sound reasoning, even if he is not Muslim. Allah, may He be glorified and exalted, has criticised the one who does it in many verses and in many Prophetic hadeeths, and He has warned the one who does it of severe punishment in this world and in the Hereafter. For more information please see the answer to question no. 97884 

Secondly: 

If a woman commits zina and becomes pregnant, it is haraam for her to abort the foetus after the soul has been breathed into it, according to scholarly consensus, even if the pregnancy resulted from zina, because it is a soul that is protected according to sharee‘ah. 

The soul is breathed into the foetus after one hundred and twenty days. 

In al-Mawsoo‘ah al-Fiqhiyyah (2/57) it says: No difference of opinion is known among the fuqaha’ concerning the prohibition on abortion after the soul has been breathed into the foetus. They stated that once the soul has been breathed into the foetus, it is haraam to abort it, according to scholarly consensus, and they unanimously stated that this is murder. End quote. 

Thirdly:

If a person commits bad deeds and is encompassed by his sins when he is in a state of kufr, such as zina, stealing or other major and deadly sins, then he becomes Muslim, Allah will forgive him for what he did when he was in a state of kufr, then he will start a new page with his Lord. Allah, may He be exalted, says (interpretation of the meaning):

“Say to those who have disbelieved, if they cease (from disbelief) their past will be forgiven”

[al-Anfaal 8:38]. 

Ibn al-‘Arabi (may Allah have mercy on him) said: Our scholars said: This is a kindness from Allah, may He be glorified, that He bestows upon His creation. That is because if the disbelievers (kuffaar) indulge in disbelief (kufr) and crimes, and they commit acts of disobedience and sins, and they cannot escape accountability, they would never be able to repent or attain forgiveness. But Allah has made it easy for them to have their repentance accepted when they turn to Him in repentance, and He bestows forgiveness upon them if they become Muslim and erases everything that has gone before; this makes it more likely that they will enter the faith and accept the word of Islam, and it serves to soften their hearts and encourage them to become Muslim. If they knew that they would be nevertheless be accountable for what they did they would not repent or become Muslim. 

End quote from Ahkaam al-Qur’aan, by Ibn al-‘Arabi, 2/398 

In Saheeh Muslim (121) it is narrated that ‘Amr ibn al-‘Aas (may Allah be pleased with him) said: when Allaah put Islam in my heart I came to the Prophet (blessings and peace of Allah be upon him) and said: Hold out your right hand so that I might swear allegiance to you. So he held out his right hand, but I withdrew my hand. He said: “What is the matter, O ‘Amr?”  I said: I want to stipulate a condition. He said, “What do you want to stipulate?” I said: That I will be forgiven. He said: “Do you not know, O ‘Amr, that Islam destroys whatever came before it?” 

An-Nawawi (may Allah have mercy on him) said: “Islam destroys whatever came before it” means: It erases it and wipes out its traces.” 

End quote from Sharh Muslim

In Fataawa ‘Ulama’ al-Lajnah ad-Daa’imah (24/296) it says:  

If a person is sincere in his repentance from his sins, even if it was associating others with Allah (shirk), zina, murder or consuming people’s wealth unlawfully, and he regrets his past sins, and restores people’s rights to them or they pardon him, and he follows that up with righteous deeds, Allah will accept his repentance and forgive his sins; indeed He will replace his bad deeds with good deeds. Allah says, describing His righteous slaves (interpretation of the meaning): 

“And those who invoke not any other ilah (god) along with Allah, nor kill such life as Allah has forbidden, except for just cause, nor commit illegal sexual intercourse and whoever does this shall receive the punishment.

The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace;

Except those who repent and believe (in Islamic Monotheism), and do righteous deeds, for those, Allah will change their sins into good deeds, and Allah is Oft-Forgiving, Most Merciful.

And whosoever repents and does righteous good deeds, then verily, he repents towards Allah with true repentance”

[al-Furqaan 25:68-71] 

“Say to those who have disbelieved, if they cease (from disbelief) their past will be forgiven”

[al-Anfaal 8:38] 

“Say: O Ibadee (My slaves) who have transgressed against themselves (by committing evil deeds and sins)! Despair not of the Mercy of Allah, verily Allah forgives all sins. Truly, He is Oft-Forgiving, Most Merciful”

[az-Zumar 39:53].

End quote. 

Shaykh ‘Abd al-‘Azeez ibn Baaz, Shaykh ‘Abd ar-Razzaaq ‘Afeefi, Shaykh ‘Abdullah ibn Qa‘ood 

With regard to the foetus that was aborted before his mother became Muslim, Allah knows best about him and what his situation will be on the Day of Resurrection. 

See also the answer to question no. 107781 

And Allah knows best.