A singularity is not a object. it is a time and position at which infinities appear in the solution of general relativity. When you speak of a "non-zero size singularity" I assume you mean a physical object inside a black hole (as could be predicted by some forms of string theory) Such objects are not part of General relativity, which models black holes as a region of spacetime including a point singularity (for a simple black hole) or a ring singularity (for a rotating black hole)
These results are consistent with General Relativity and two merging Kerr black holes (which have a ring singularity in GR).
They would also be consistent with other models of gravity, including models in which a physical singularity doesn't form. But there is no positive evidence here for there being an object that is a millionth of an angstrom behind the event horizon.
I'm not sure what you mean by "binary singularities distanced by a few microns" The amplitude of the gravitational waves detected was much smaller than that, and there is nothing about microns in the linked video.
We would not expect the signal to continue to increase in frequency up to 90KHz. A new single event horizon forms at some point, in this case when the gravitational waves have reached about 200Hz. A short "ring down" period follows the merger as a single black hole settles into a new stable state.
The objects measured by LIGO are black holes, with an event horizon about 20km in diameter. The measurements at LIGO don't suggest that any object exists inside the black hole. Nothing in these data suggest the objects were the size of electrons.
The mass estimates have quite large error bars, for the first Gravitational wave detected, the masses were about 30 solar masses +- 4solar masses, with similar uncertainties in the Schwartzchild radii
See the orginal LIGO article https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.116.061102