How does inflation relate to spontaneous matter creation? According to Inflation for Beginners,

... quantum physics allows the entire Universe to appear, in this supercompact form, out of nothing at all, as a cosmic free lunch. The idea that the Universe may have appeared out of nothing at all, and contains zero energy overall, was developed by Edward Tryon, of the City University in New York, who suggested in the 1970s, that it might have appeared out of nothing as a so-called vacuum fluctuation, allowed by quantum theory.

Based on my layman's understanding, quantum mechanics allows for energy to spontaneously appear, provided it disappears later. But matter, with its positive energy, is offset by the negative energy gravitational field it creates -- netting zero energy that therefore doesn't have to disappear.
Does this mean that matter/antimatter (say, an electron and a positron) may be created and annihilate each other, or maybe some amount of matter on its own (with gravity and thus a net energy of zero) could appear and exist forever? In the latter case, how does a small amount of matter compare with this supercompact form that leads to inflation? Presumably there are isolated hunks of matter with corresponding gravity out there that quantum mechanics created but that didn't expand into their own universes?
 A: 
Does this mean that matter/antimatter (say, an electron and a positron) may be created and annihilate each other,

This is called vacuum fluctuations as stated by Quantum Field Theory. In this case energy has to be supplied so that the electron positron pair out of the vacuum would materialize. This does  happen at laboratory energies in experiments with strong laser beams . It is also   supposed to happen with the energy supplied by the gravitational field of black holes, one lepton falling in the black hole the other leaving: Hawking radiation

or maybe some amount of matter on its own (with gravity and thus a net energy of zero) could appear and exist forever? In the latter case, how does a small amount of matter compare with this supercompact form that leads to inflation? Presumably there are isolated hunks of matter with corresponding gravity out there that quantum mechanics created but that didn't expand into their own universes?

You must not have read the article you link to the end:

The idea of chaotic inflation led to what is (so far) the ultimate development of the inflationary scenario. The great unanswered question in standard Big Bang cosmology is what came "before" the singularity. It is often said that the question is meaningless, since time itself began at the singularity. But chaotic inflation suggests that our Universe grew out of a quantum fluctuation in some pre-existing region of spacetime, and that exactly equivalent processes can create regions of inflation within our own Universe. In effect, new universes bud off from our Universe, and our Universe may itself have budded off from another universe, in a process which had no beginning and will have no end. A variation on this theme suggests that the "budding" process takes place through black holes, and that every time a black hole collapses into a singularity it "bounces" out into another set of spacetime dimensions, creating a new inflationary universe -- this is called the baby universe scenario. 

So in the active research front of cosmology model spontaneous gravitational creations are being proposed. 
