Is the fast of a woman valid if she experiences secretions after reciting the Quran and having a memory of sexual intercourse cross her mind, knowing that she subsequently performed ghusl and prayed Fajr, and is expiation due upon her?

Fasting is not invalidated by secretions resulting from mere thoughts, and no expiation is due for them, whether the discharge is madhy (pre-seminal fluid) or manyy (seminal fluid). The general rule for fluid discharged after thinking about intercourse is that it is madhy, and it requires washing it off and performing ablution (wudu'). A full ritual bath (ghusl (definition)) is only obligatory if there is certainty of the emission of manyy.