We investigate the feasibility of dark matter particles existing in the Universe as a spin-$12$ fermion using effective field theories to parametrise the higher order physics. Our goal is to determine the requirements for exclusion of such particles by direct and indirect detection. In part~\ref{part:1}, based on ref.~\cite{geytenbeek21}, we introduce a complete basis of operators up to dimension 5 for fermions that are part of singlet, doublet and triplet representation of the Standard Model $SU(2)$ electroweak symmetry group. Such particles correspond to the bino, higgsino and wino of supersymmetry models respectively. We determine the thermal relic density of particles interacting with each of our operators and show that viable thermal relics that evade experimental constraints can exist with masses as low as as $100\backslash GeV$ and up to $10\backslash TeV$ due to the mass splittings that arise at dimension 5. In part~\ref{part:2}, based on ref.~\cite{geytenbeek17} we further investigate the effect of fermionic dark matter that may interact through an electromagnetic dipole interaction at dimension 5 on energy transport in the Sun. In particular, we test whether the models can provide a solution to the solar abundance problem, a theoretical discrepancy between the observations of helioseismology and the theoretical Standard Solar Model. We introduce all of the necessary theoretical implementation and show that, although introducing dark matter may alleviate the tension of the solar abundance problem, the required interaction strengths are strongly ruled out by direct detection experiments.