Is the one afflicted with obsessive whispers forgiven if he ignores his whispers, and is it obligatory to repeat the prayer when in doubt about its conclusion?

The cure for obsessive thoughts (waswas) is to ignore them and pay them no attention. If you disregard them and turn away from them, you will be doing what Allah has commanded, and your acts of worship will be valid and rewarded. Doubt about an act of worship after completing it does not affect its validity.