A triangular based pyramid has zero pairs of parallel faces. In a triangular based pyramid, all three faces of the base are not parallel to the apex, which means there are no pairs of parallel faces in this type of shape.
ZERO!
ZERO!
Zero parallel faces in a triangular pyramid. There are four faces, and none of them are parallel to each other.
Zero
A trapezoid (in most cases)
a circle
An isosceles triangle has no parallel sides but it does have 2 sides of equal lengths
a cylinder
Your question is inconsistent on its face. You asked "What shape has zero faces . . . . . and has only one face." I'd say that nothing could ever meet both of those requirements. They are ... how you say ... 'mutually exclusive'.
The carbon is in the middle; this is a tetrahedral shape, and there are zero lone pairs.
There are zero faces in a sphere.