How can one get rid of the intrusive thoughts that relate to Islam's permitting of certain matters, and to God Almighty's ability to see and hear all His creation, and to the reason for God's questioning of the angels despite His knowing everything, which affect the serenity of worship?

The cure for obsessive thoughts is to turn away from them and not pay them any attention. Your dislike of them is a sign of true faith. As for people turning away from religion, this should be a motivation to teach them and call them to Allah, instead of being a cause for obsessive thoughts.