To answer your first question -- yes, matter and antimatter can exist
together, if only briefly. There is a trivial case of photons -- they
are their own antiparticles (that's kinda cheating, I know). Also,
antineutrinos zip around just as much as neutrinos and don't annihilate
(at least not too often) because the interaction probability is so darn
low. Other matter-antimatter combinations can last for some short
amounts of time -- an electron and a positron can orbit each other in a
state that resembles a hydrogen atom state, called "positronium". It
doesn't last too long, though; the electron and positron annihilate to
photons.
Quarks and antiquarks can also coexist within bound states. Pions
are particles made up of a quark and an antiquark stuck toghether with
the strong nuclear force. They too decay by annihilation when the
quarks are antiparticles of each other, and by the weak interaction if
the quarks are matter and antimatter but have different charges and
cannot annihilate to photons.
I don't see where the imbalance comes from in your scenario. In
particular, we need to explain why only one kind of matter (and not
antimatter) is dominant in the universe, when we know that if the
universe was very, very hot at one time, then there were exactly or at
least approximately equal amounts of each kind. It is known now that
matter and antimatter don't behave exactly the same way (look under "CP
Violation" on the web for more info); we are still studying this kind
of effect and still don't have all the answers to why there is so much
more matter than antimatter in the universe.
Tom
(published on 10/22/2007)