  In this paper, we explore the intriguing interplay between fundamental
theoretical physics concepts within the context of charged black holes.
Specifically, we focus on the consistency of the weak gravity conjecture (WGC)
and weak cosmic censorship conjecture (WCCC) in the thermodynamics of conformal
field theory (CFT), and restricted phase space (RPS) for AdS
Reissner-Nordstr$\"o$m black holes with a perfect fluid dark matter (RN-PFDM).
The WGC ensures that gravity remains the weakest force in the system.
Meanwhile, the WCCC addresses the cosmic censorship problem by preventing the
violation of fundamental physical laws near the black hole singularity. First,
we analyze the RN black hole's free energy in both spaces, revealing a
distinctive swallowtail pattern indicative of a first-order phase transition
when certain free parameter conditions are met. We explore the WGC across
different phase spaces, emphasizing the need for certain conditions in EPST,
RPST, and CFT. We demonstrate that PFDM $( \gamma )$ and the radius of AdS
($l$) have a vital role in proving the satisfaction of the WGC. Also, these
values have a linear relation with the range compatibility of WGC. The range of
compatibility for WGC in RPST and EPST is the same while for CFT, this range is
larger than EPST, and RPST. It means somehow the WGC and CFT are more
consistent. The WCCC was examined at the critical juncture, confirming its
validity with $( f(M_c, Q_c, r_c) = 0 )$. We conclude that the WGC is supported
at the critical point of black holes, and the WCCC is also maintained,
demonstrating the robustness of these conjectures within the critical ranges of
black hole parameters.
