Does one become an infidel who finds a coin with the name of Allah on it in a restroom and leaves it on a partition wall between two restrooms, or places it there himself?

There is no harm in entering the restroom with money in one's pocket. As for the riyal on the wall dividing the two restrooms, it is not considered to be inside either of them. It is preferable to take it, fearing its fall or because it is a minor lost item (luqatah) that its owner would not pursue. One must be careful not to associate disbelief (kufr) with such simple matters, as it might be a whisper from Satan (waswasah).