The Higgs does not play that kind of role. It is a common misconception, since Higgs it often referred to as "giving mass to the other particles", which is true, and called the Higgs-mechanism, it does not influence the curvature of space-time that way. That is all due to the graviton (assuming, which it is also commonly believed, that gravity is quantised).
Mass is one thing, interactions between masses another.
Gravity at black holes’s event horizon is not quite coming from where you think it is: it isn’t ”emitted by” or ”emanating from” the singularity. Rather, as gravity is a form of energy, and mass-energy creates gravity, the gravitational field at the border, within our observable universe, is intense enough to whip itself up into a self-maintaining recursive but sustainable loop. No communication from what lies within the event horizon is neither possible nor required.
I still don't quite get "the gravitational field at the border, within our observable universe, is intense enough to whip itself up into a self-maintaining recursive but sustainable loop" (especially the self-maintaining, recursive part. How?), but I guess one would need a good understanding of GR to go beyond this level?
"[...] the electromagnetic repulsion or attraction between two charges—can be thought of as due to the exchange of many virtual photons between the charges."
so when the electromagnetic force mediation takes place, it exchanges virtual photons, and this is different from an object exchanging physical photons with another (which we would more think of as one object shining (if the photon is in the visible spectrum) on another).
How a virtual graviton would interact between BHs and other particles are up to any suggested theory for quantum gravity to explain.
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/... https://www.quora.com/in/If-both-the-photon-and-the-graviton...
What I am trying to describe is the inherent nonlinearity of general relativity, wherein compound solutions cannot be obtained simply summing up or overlaying simpler situations: the gravity filed itself generates more gravity, so it can recursively reach and sustain a critical value.
This is a non sequitur, presumably due to a misunderstanding caused from some pop sci article. You really do not need gravitons to describe any of the dynamics of "pulling matter in" (at least for "usual" black holes), and there is no "pushing out gravitons" involved.