>>2585
I don't think there's any direct proof that inertial mass = gravitational mass yet. But so far we haven't found any discrepancy between them. So yeah your question does make sense.
But, as far as I'm aware, the proposition that it's impossible to tell difference between uniform acceleration and uniform gravity field (equivalent to the statement that inertial and gravitational mass are equivalent) is also one of the core propositions of general relativity.
Anyway, the biggest problem of origin of mass through Higgs field is that the Higgs boson will interact with vacuum, forming particles that further interact with Higgs field, so without some renormalisation (with supersymmetry, for example) the mass diverges to infinity. Or it should at least be on order of Planck mass, which is way more than the observed.
>>2587
It's either this (which is mathematically simpler to understand, but it won't help you how to imagine it), or to imagine virtual particles which should generally not be there. You can imagine the vacuum as a soup of short-lived virtual particles that can interact with matter, but since they're virtual, their lifetime exponentially decreases with their energy. So when a particle moves through empty space, it will bump into and interact with non-existent Higgs bosons, which are the only particles that actually do have mass (because their mass is directly defined my Higgs field vacuum value, presumed to be constant). It's essentially a scalar field (directionless) that slows down particles that move through it, like a viscous fluid slows down a falling rock.