Is it obligatory for a woman who experienced a wet dream and woke up without having masturbated, but then doubted whether she had done so while asleep, to perform ghusl and make up her prayers and fasting?

A wet dream necessitates ghusl if semen is discharged. However, a wet dream without discharge does not necessitate ghusl. Fasting is not invalidated by a wet dream whatsoever, whether semen is discharged or not. When in doubt about the discharge of semen or the act of masturbation, the default is that there was no discharge or no act, and therefore ghusl is not required, nor is making up the fast, unless there is certainty.