  We investigate the possibilities for probing MeV dark matter (DM) particles
and primordial black holes (PBHs) (for masses $\sim 10^{15}$--$10^{17}$ g) at
the upcoming radio telescope SKA, using photon signals from the Inverse Compton
(IC) effect within a galactic halo. Pair-annihilation or decay of MeV DM
particles (into $e^+ e^-$ pairs) or Hawking radiation from a population of PBHs
generates mildly relativistic $e^{\pm}$ which can lead to radio signals through
the IC scattering on low energy cosmic microwave background (CMB) photons. We
study the ability of SKA to detect such signals coming from nearby ultra-faint
dwarf galaxies Segue I and Ursa Major II as well as the globular cluster
$\omega$-cen and the Coma cluster. We find that with $\sim 100$ hours of
observation, the SKA improves the Planck constraints on the DM
annihilation/decay rate and the PBH abundance for masses in the range $\sim 1$
to few tens of MeV and above $10^{15}$ to $10^{17}$ g, respectively.
Importantly, the SKA limits are independent of the assumed magnetic fields
within the galaxies. Previously allowed regions of diffusion parameters of MeV
electrons inside a dwarf galaxy that give rise to observable signals at the SKA
are also excluded. For objects like dwarf galaxies, predicted SKA constraints
depend on both the DM and diffusion parameters. Independent observations in
different frequency bands, e.g., radio and $\gamma$-ray frequencies, may break
this degeneracy and thus enable one to constrain the combined parameter space
of DM and diffusion. However, the constraints are independent of diffusion
parameters for galaxy clusters such as Coma.
