What is the ruling on intrusive thoughts during prayer? And what is the ruling on shaving hair in a way that one fears might be considered Qaza’ (partial shaving)?

You address the intrusive thoughts during prayer by focusing with devotion, contemplating what the worshiper or imam recites, and by supplicating, earnestly appealing to Allah, and seeking refuge in Him. Uthman ibn Abi al-As reported: "O Messenger of Allah, the devil has intervened between me and my prayer and my recitation." The Messenger of Allah, peace and blessings be upon him, said: "That is a devil called Khanzab. If you sense him, seek refuge in Allah from him and spit to your left three times."

As for shaving: Trimming and thinning the sides of the head's hair does not fall under the forbidden qaza'. However, shaving part of the head's hair and leaving other parts is disliked because it is a form of the forbidden qaza', which includes shaving scattered areas, or shaving the middle and leaving the sides, or vice versa, or shaving the front and leaving the back.