In the corner: The apple is in the corner of the room/box/container. On the corner: The apple is on the corner of the table/street/location. Hope this helps. =)

It can depend on whether the location is 'open' or 'closed'. For example, if you are talking about a room, you would say that something or someone is in the corner eg 'The bookcase is in the corner of the room'. The same with a page or a screen eg 'Click on the icon in the corner of your screen'. However, in an open location, such as a street, you could say 'on the corner' eg 'Meet me on the corner of King Street.'

In English we do not distinguish between Rincon and Esquina. In your first example "Corner" would be "Rincon" and in your second it would be "Esquina."