  As part of the T-REX project, a number of R&D and prototyping activities have
been carried out during the last years to explore the applicability of
Micromegas-read gaseous TPCs in rare event searches like double beta decay
(DBD), axion research and low-mass WIMP searches. While in the companion paper
we focus on DBD, in this paper we focus on the results regarding the search for
dark matter candidates, both axions and WIMPs. Small ultra-low background
Micromegas detectors are used to image the x-ray signal expected in axion
helioscopes like CAST at CERN. Background levels as low as $0.8\times 10^{-6}$
c keV$^{-1}$cm$^{-2}$s$^{-1}$ have already been achieved in CAST while values
down to $\sim10^{-7}$ c keV$^{-1}$cm$^{-2}$s$^{-1}$ have been obtained in a
test bench placed underground in the Laboratorio Subterr\'aneo de Canfranc.
Prospects to consolidate and further reduce these values down to $\sim10^{-8}$
c keV$^{-1}$cm$^{-2}$s$^{-1}$will be described. Such detectors, placed at the
focal point of x-ray telescopes in the future IAXO experiment, would allow for
10$^5$ better signal-to-noise ratio than CAST, and search for solar axions with
$g_{a\gamma}$ down to few 10$^{12}$ GeV$^{-1}$, well into unexplored axion
parameter space. In addition, a scaled-up version of these TPCs, properly
shielded and placed underground, can be competitive in the search for low-mass
WIMPs. The TREX-DM prototype, with $\sim$0.300 kg of Ar at 10 bar, or
alternatively $\sim$0.160 kg of Ne at 10 bar, and energy threshold well below 1
keV, has been built to test this concept. We will describe the main technical
solutions developed, as well as the results from the commissioning phase on
surface. The anticipated sensitivity of this technique might reach
$\sim10^{-44}$ cm$^2$ for low mass ($<10$ GeV) WIMPs, well beyond current
experimental limits in this mass range.
