If a woman had an abortion while an Atheist, then became Christian, and decided to become Catholic, could she ever receive Sacraments?
Sure. Why not? A woman who has an abortion while Catholic incurs an excommunication, but it can be lifted by her Bishop if she repents.
Yes, of course.
She will receive the sacraments along with any and all other repentant souls who are trusting in the mercy of Christ to cleanse them from their past sins, and perfecting themselves in cooperation with the Holy Spirit, through on-going conversion, to become worthy of the promises of Christ .
She will attend RCIA and at the Easter vigil receive the sacraments. If she has already been baptized, she will receive the sacrament of reconciliation (confession). Her confession of the abortion to the priest will result in absolution and mercy.
If she is not baptized, then the abortion will be cleansed in the renewing waters. She will not need to confess the abortion if she is being baptized, because she will reject Satan and all of his works at that time, but she still may want to talk to a priest for the psychological benefit after she is baptized.
Interesting, thank you.