What is the ruling on placing the Mushaf in mosques on shelves, especially if they are low, below the navel?

Mushafs must be preserved by placing them in suitable locations that befit their status. There is no specific required height; the important thing is that they are not debased by being placed in an unclean or disrespectful location, and that they are not placed directly on the ground. Instead, they must be elevated, even if slightly.