Are the intrusive thoughts that a suitor experiences about wronging his fiancée and divorcing her, in addition to the dreams he sees, a result of the Istikhara prayer or from the whispers of Satan, and what should he do to avoid that?

Istikhara is seeking what is best and submitting to the command of Allah. If you perform istikhara and your heart feels at ease, then proceed with what you sought guidance for, such as marrying this religious girl; she is a treasure that must be won. What you mentioned about self-talk and dreams is from the whispers of Satan, so seek refuge in Allah from him and do not pay attention to it.