According to the Wikipedia page on the electron:


  The electron has no known substructure. Hence, it is defined or assumed to be a point particle with a point charge and no spatial extent.


Does point particle mean the particle should not have a shape, surface area or volume?

But when I searched Google for the "electron shape" I got many results (like this and this) that says electrons are round in shape.

As far as we know the electron is a point particle - this is addressed in the question Qmechanic suggested: What is the mass density distribution of an electron?

However an electron is surrounded by a cloud of virtual particles, and the experiments in the links you provided have been studying the distribution of those virtual particles. In particular they have been attempting to measure the electron electric dipole moment, which is determined by the distribution of the virtual particles. In this context the word shape means the shape of the virtual particle cloud not the shape of the electron itself.

The Standard Model predicts that the cloud of virtual particles is spherically symmetric to well below current experimental error. However supersymmetry predicts there are deviations from spherical symmetry that could be measurable. The recent experimentals have found the electric dipole moment to be zero, i.e. the virtual particle cloud spherically symmetric, to an accuracy that is challenging the supersymmetric calculations.

However there are many different theories based upon supersymmetry, so the result doesn't prove supersymmetry doesn't exist - it just constrains it.
