Are elementary particles actually more elementary than quasiparticles? Quarks and leptons are considered elementary particles, while phonons, holes, and solitons are quasiparticles. 
In light of emergent phenomena, such as fractionally charged particles in fractional quantum Hall effect and spinon and chargon in spin-charge separation, are elementary particles actually more elementary than quasiparticles? 
Does the answer simply depend on whether one is adopting a reductionist or emergent point of view? 
 A: As you mention fractional quantum Hall  effect, let me consider a system of $N$ electrons typical of a condensed matter system. Now think of your Hamiltonian as having two parts 
$\hat{H} =\hat{H}_0+\hat{H}_{int}e^{-\zeta t}$ with $t >0$
so that you gradually switch-off the interacting part so that at large times you can map your complete Hamiltonian (with interactions) to your free Hamiltonian. If you can do that, the matrix elements of the interacting and non-interacting case will be identical.
In the Fermi liquid theory, the quasiparticles are understood as the excitations of an interacting many-body system. They correspond to the creation or annihilation of particles [electrons] and can be labeled by the same quantum numbers as the non-interacting states provided that:


*

*The adiabatic procedure is valid (that is the energy of the state larger than the rate of change, $\varepsilon_{\mathbf{k}\sigma} \ll \zeta $, which is equivalent to assuming that $T\ll\zeta$ since typically $\varepsilon_{\mathbf{k}\sigma}\simeq T$.

*The interactions do not induce transitions of the states in question, or in
other words the life-time of the state must satisfy $\tau_{\text{life}} \gg \zeta^{-1}$. 


Thus the quasiparticle concept only makes sense on time scales shorter than the quasiparticle life time and we must not thought of them as the exact eigenstates. On the other hand, electrons have infinite life time (understand infinite by very very large $\tau_{\text{life,e}}\simeq10^{26}$ years). The proper "elementary" particles are the electrons, not the quasiparticles. Again, quasiparticles refers just to the excitations of the system. Obviously, some properties of your system will be described only via the excitations of the whole system, these are the emergent properties you were talking about (fractional charge, fractional statistics...). 
D.
A: Elementary particles, like photons and electrons, are not more elementary in the sense that there are underlying theories, such as quantum spin model on lattice, from which they can be derived as an effective approximation (see for example arXiv:hep-th/0302201). 
In particular, the string-net condensation provides a unified origin for gauge interactions and Fermi statistics:
Both elementary gauge bosons (such as photons, gluons) and elementary fermions (such as electrons, quarks) can emerge as quasi-particles in a quantum spin model on lattice
if the  quantum spin model has a "string-net condensed state" 
as its ground state. An comparison between the string-net approach and the
superstring approach can be found here.
There is a falsifiable prediction  from the  string-net theory:
all fermions (elementary or composite) must carry gauge charges (see cond-mat/0302460).
The standard model contain composite fermions that are neutral for $U(1)\times SU(2)\times SU(3)$ gauge theory. So according to the string-net theory, the
standard model is incomplete. The correct model should contain extra gauge theory, such as a $Z_2$ gauge theory. So the string-net theory predicts extra
discrete gauge theory and new cosmic strings associated with the new discrete gauge theory.
The emergence approach may also produce (linear) quantum gravity from quantum spin models (see arXiv:0907.1203).
However, the emergence approach (such as the string-net theory), so far, fail to produce the chiral coupling between the $SU(2)$ weak interaction and the fermions.
A: They are more elementary in the sense that there is no accepted underlying theory from which they can be derived as an effective approximation.
On the other hand, what is elementaty changes with time. At some time, protons and neutrons were considered to be elementary particles, whily they are now considered to be composed of quarks. There are various hypothetical theories in which the particles currently viewed as elementary are considered to be composed of even more elementary particles. The latter are called preons. See http://en.wikipedia.org/wiki/Preon
Thus if one of the preon theories would gain major acceptance, the currently accepted elementary partricles would get the status of quasiparticles of an effective theory (that would be the current standard model) deduced by coarse graining from the underlying preon theory.
A: Quasiparticles exist only in condensed matter. Real particles can propagate also in vacuum. If you have an underlying medium in your modell for vacuum where you can describe the known real particles as emergent quasiparticles of some yet unknown real particles, this is another thing. 
