A friend of mine said to me that a baby born from a demon possessed parents is likely to be possessed as well. I totally disagreed with him in several points:
1. The child received the Holy Spirit during the Sacrament of Confirmation and has been partaking of the Lord's Body and Blood.
2. God would never ever let that happen.
3. The child has free will.
A baby born from demon possessed parents is NOT likely to be possessed for the three reasons that you mentioned.
In the unfortunate situation where both parents are demon possessed, most likely they would not allow their child to be baptized. Everyone born into this world does not yet have God's grace. Thus, the Coptic Orthodox Church strongly advocates for infant baptism. If the parents allow someone else, i.e., a godparent to take the responsibility of their child's spiritual life, then the child can receive the Holy Mystery of Baptism.
During the baptismal prayers, the devil and his armies are denounced, and the acceptance of the Lord Jesus Christ is declared. In the Coptic Orthodox Church, the newly baptized person immediately receives the Holy Mystery of Confirmation by Chrismation of the Holy Myron Oil, and partakes of the Holy Mystery of the Eucharist.
The question is then; can someone who was already baptized become demon possessed? The answer is that it is possible if one refuses to regularly submit to the Holy Spirit, repent, and partake of the Holy Mystery of the Eucharist. When the baby grows up and is aware and responsible for his actions, but chooses to resist the Holy Spirit, demon possession might happen if he leaves himself exposed to this evil.
We must be on our guards at all time. Judas fell into Satan's hands even after all that he eye-witnessed. Demas deserted St. Paul after many travels and returned to the world (2 Timothy 4:10). People can easily fall prey into Satan's hands if they are not watchful, prayerful, and faithful to a life of repentance and to the Lord Jesus Christ. We must be vehemently committed to the sacramental life that shields us from the devil's clutches. Though the fight can be fierce, the choice is ours and God will help us if we ask Him. As for children, it is imperative that if their parents are negligent to their child's spiritual welfare, then friends and family need to step in and persuade them to allow their child to have the opportunity for a wholesome spiritual life through a godparent.
"Therefore submit to God. Resist the devil and he will flee from you" (James 4:7).