Finding Luna's belongings -

One of her items is in the Viaduct entrance next to the bookshelf and the stuttering portrait. Another one is located in the Courtyard before the covered bridge, directly in front of the fountain.

Using spells on objects -

Any time you see any object begin to light up, cast spells until you find the correct one, then do it again on the others. If you see a student light up, hold R1 and cast a dueling spell.