  In this paper we first develop various enhancements of the theory of spectral
invariants of Hamiltonian Floer homology and of Entovi-Polterovich theory of
spectral symplectic quasi-states and quasimorphisms by incorporating \emph{bulk
deformations}, i.e., deformations by ambient cycles of symplectic manifolds, of
the Floer homology and quantum cohomology. Essentially the same kind of
construction is independently carried out by Usher [Us4] in a slightly less
general context. Then we explore various applications of these enhancements to
the symplectic topology, especially new construction of symplectic
quasi-states, quasimorphisms and new Lagrangian intersection results on toric
manifolds. The most novel part of this paper is to use open-closed
Gromov-Witten theory (operator $\frak q$ in [FOOO1] and its variant involving
closed orbits of periodic Hamiltonian system) to connect spectral invariants
(with bulk deformation), symplectic quasi-states, quasimorphism to the
Lagrangian Floer theory (with bulk deformation). We use this open-closed
Gromov-Witten theory to produce new examples. Especially using the calculation
of Lagrangian Floer homology with bulk deformation in [FOOO3,FOOO4], we produce
examples of compact toric manifolds $(M,\omega)$ which admits uncountably many
independent quasimorphisms $\widetilde{\operatorname{Ham}}(M,\omega) \to
\mathbb R$. We also obtain a new intersection result of Lagrangian submanifolds
on $S^2 \times S^2$ discovered in [FOOO6]. Many of these applications were
announced in [FOOO3,FOOO4,FOOO6].
