Is there a way of labeling the number of points with the same coordinates?

Nice question! PyQGIS to the rescue!

Follow these steps to get a new field (in your original layer) called label with the number of points that lie in the same location:

1. Active (select) your layer in the QGIS ToC.

2. Run this code snippet in the QGIS Python console:

   from PyQt4.QtCore import QVariant
   
   lyr = iface.activeLayer()
   
   # Create New Field
   lyr.dataProvider().addAttributes([QgsField("label", QVariant.Int)])
   lyr.updateFields()
   fIdx = lyr.fieldNameIndex( 'label' )
   
   # Create Spatial Index
   idx = QgsSpatialIndex()
   for f in lyr.getFeatures():
     idx.insertFeature(f)
   
   # Use the Spatial Index
   attrFeatMap = {}
   for f in lyr.getFeatures():
     if not f.id() in attrFeatMap:
       res = idx.intersects( f.geometry().boundingBox() )
       for id in res:
          attrFeatMap[id] = { fIdx : len(res) }
   
   # Write calculated count to the label field
   lyr.dataProvider().changeAttributeValues( attrFeatMap )
   

3. Open layer properties and configure labels selecting the label field we've just populated.

4. This is the result:

   

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EDIT:

As you would also like to filter by an attribute, you can define an expression in the beginning of the code (for example, after the Create New Field block):

expr = QgsExpression( '"string"=\'{}\''.format("abc") )

and replace the two calls to lyr.getFeatures() by:

lyr.getFeatures( QgsFeatureRequest( expr ) )

That way you'll only get the count of the points with the same coordinates that fulfill the string=abc condition.

If I understand, you want aggregate a layer by location. You will need SQL for that, so create a virtual layer (Qgis >= 2.14) with a query like :

SELECT geometry, count(*) AS count FROM your_layer GROUP BY geometry

You can now use the "count" field of the virtual layer as label.

For adding the filter by the text field :

SELECT 
  geometry, 
  count(*) AS count_total,
  count(CASE WHEN filter_field = "abc" THEN 1 ELSE NULL END) as count_filter
FROM your_layer GROUP BY geometry

Adapt words to your layer : your_layer, filter_field and "abc".

you can use Rule-based labeling

shapefile point before the rule

all the points they label.

after the rule:

using rules you can specify which labels to show, even using conditional statements