  We extend previous inelastic neutron scattering results on the geometrically
frustrated antiferromagnet hexagonal-YMnO$_3$, which has been suggested to
belong to the class of classical spin liquids. We extend the energy transfer
coverage of the diffuse signal up to 6.9 meV within a wide temperature range
around the ordering temperature, $T_\mathrm{N}$. The two distinct diffuse
signals in the a-b plane, the signal localized at $\Gamma$' and the scattering
intensity connecting $\Gamma$' points over the M', are shown to be only weakly
energy dependent. In addition, an external magnetic field of up to 10.5 T
applied along c is shown to have no effect on the diffuse signal. In the
orthogonal scattering plane, the signals are shown to be dependent on l only
through the magnetic form factor, showing that the correlations are purely
two-dimensional, and supporting its origin to be the frustrated Mn$^{3+}$
triangles. This result is corroborated by atomistic spin dynamics simulations
showing similar scattering vector and temperature behaviours. Lastly, data for
the spin wave scattering in the (h, 0, l) plane allow for a discussion of the
magnetic ground state where better agreement is found between the data and an
ordered structure of the $\Gamma_1$ or $\Gamma_3$ symmetry, albeit crystal
electric field arguments dismisses the $\Gamma_1$ as possibility.
