No, the pixel coordinates of used paintings is in the game code.
The only one in the pic you posted is the 4x4 painting on the right of the two on the bottom, which was added in an update not too long ago (You'll notice ingame you sometimes place a violet 4x4 painting)
In the given images above taken from Gerudoku's Texture Pack, which I am currently using in my own Texture Pack Collection.
If I add new image designs on the pink spaces available, will they be available for use in game?
Thanks Much,
The only one in the pic you posted is the 4x4 painting on the right of the two on the bottom, which was added in an update not too long ago (You'll notice ingame you sometimes place a violet 4x4 painting)