Is it obligatory to repeat the ‘Umrah, offer an expiation (kaffarah), or make a sacrifice (hady) if one performs ‘Umrah without completing the ‘Ishā’ prayer with the intention of repeating it, and without lowering one’s gaze from women?

Your Umrah (definition) and your Isha prayer are valid, and you are not required to repeat them. There is no connection between the validity of your prayer and the Umrah. The cure for obsessive thoughts (waswasa) is to turn away from them and not pay attention to them. Whenever Satan casts into your heart that your worship is invalid, turn away from that and proceed with your worship. Strive in supplication, and you can consult doctors and the counseling department.