Is it permissible for an Islamic Studies teacher in an "international" school to evaluate a student using the phrase: "Believes in Allah Almighty, and recognizes His names and attributes, inferring His existence from the manifestations of His power"?

There is no objection to the mentioned text; for the observable manifestations of God's power are evidence of His existence, and His verbal and visual signs indicate His names, attributes, oneness, commands, and prohibitions, as mentioned by Ibn Al-Qayyim.