  Time-dependent density functional theory (TDDFT) within the linear response
regime provides a solid mathematical framework to capture excitations. The
accuracy of the theory, however, largely depends on the approximations for the
exchange-correlation (xc) kernels. Away from the long-wavelength (or $q=0$
short wave-vector) and zero-frequency ($\omega=0$) limit, the correlation
contribution to the kernel becomes more relevant and dominant over exchange.
The dielectric function in principle can encompass xc effects relevant to
describe low-density physics. Furthermore, besides collective plasmon
excitations, the dielectric function can reveal collective electron-hole
excitations, often dubbed ``ghost excitons.'' Beside collective excitons, the
physics in the low-density regime is rich, as exemplified by a static
charge-density wave that was recently found for $r_\mathrm{s} > 69$, and was
shown to be associated with softening of the plasmon mode. These excitations
are seen to be present in much higher density 2D HEGs, of $r_\mathrm{s} \geq
4$. In this work we perform a thorough analysis with xc model kernels for
excitations of various nature. The uniform electron gas as a useful model of
real metallic systems is used as a platform of our analysis. We highlight the
relevance of exact constraints as we display and explain screening and
excitations in the low-density region.
