With RadDiagram it's possible to have a shape connected to it self through ConnectionsCollection DiagramConnection declaration. 

But it would be nice if the diagram end user, using the built-in drag and drop could connect a shape to it self like it does between different shapes.

Thanks

It will be possible to retrieve the pointer coordinates when using the OnMouseEnter and OnMouseLeave events of RadDiagram via their event object.

Allow shapes to be dragged and dropped between 2 diagram controls (and fire the associated drag-drop events on the target diagram container).

A connector that is only connected to one shape cannot be imported via JSON.
Tested here:
http://demos.telerik.com/aspnet-ajax/diagram/examples/saveload/defaultcs.aspx

JSON:
{
    "shapes": [{
        "id": "nadal_winner",
        "background": "#f18100",
        "hover": {
            "opacity": 0.2
        },
        "cursor": "pointer",
        "content": {
            "align": "center middle",
            "text": "R. Nadal",
            "color": "#fff"
        },
        "selectable": true,
        "serializable": true,
        "enable": true,
        "type": "rectangle",
        "path": "",
        "visual": null,
        "x": 180,
        "y": 155,
        "minWidth": 20,
        "minHeight": 20,
        "width": 140,
        "height": 30,
        "connectors": [{
            "name": "Top",
            "description": "Top Connector"
        }, {
            "name": "Right",
            "description": "Right Connector"
        }, {
            "name": "Bottom",
            "description": "Bottom Connector"
        }, {
            "name": "Left",
            "Description": "Left Connector"
        }, {
            "name": "Auto",
            "Description": "Auto Connector"
        }],
        "rotation": {
            "angle": 0
        },
        "stroke": {
            "width": 0,
            "color": "#fff"
        },
        "connectorDefaults": {
            "background": "#444444",
            "stroke": {
                "color": "white"
            },
            "hover": {
                "background": "white",
                "stroke": {
                    "color": "#444444"
                }
            }
        },
        "undoable": false
    }],
    "connections": [{
        "from": {
            "shapeId": "nadal_winner",
            "connector": "Right"
        },
        "to": "OK6oDroWug",
        "id": "OK6oDroWug",
        "background": "Green",
        "hover": {
            "stroke": {}
        },
        "cursor": "pointer",
        "content": {
            "align": "center middle",
            "text": "",
            "color": "#444444"
        },
        "selectable": true,
        "serializable": true,
        "enable": true,
        "startCap": "none",
        "endCap": "none",
        "points": [],
        "stroke": {
            "width": 2,
            "color": "#6c6c6c"
        },
        "select": {
            "handles": {
                "width": 8,
                "height": 8,
                "background": "white",
                "stroke": {
                    "color": "#444444"
                }
            }
        }
    }]
}