See playlist for all videos. Numbers on each one below match numbers in the videos. You only need lumos and basic cast for most of these. The others will note what you need. For example you’ll need depulso for the one behind the Map of Argyllshire #10). For others, you’ll need level 1 Alohomora, which you get from The Caretaker’s Lunar Lament quest.
Basic Moth Puzzle Solution: Use lumos to reveal the picture in the frame, find the moth, use lumos to lure it back to the frame, and then use basic cast to put the missing moth back into the frame.
Moth Puzzles Playlist on Youtube