This paper explores the interplay between fundamental theoretical physics concepts, focusing on the consistency of the Weak Gravity Conjecture (WGC) and the Weak Cosmic Censorship Conjecture (WCCC) in the thermodynamics of charged black holes within the context of conformal field theory (CFT) and restricted phase space (RPS). The study specifically examines Reissner-Nordström (RN) black holes surrounded by perfect fluid dark matter (RN-PFDM). Key findings include: 1. **Thermodynamic Analysis**: The free energy of RN-AdS black holes in the presence of PFDM exhibits a distinctive swallowtail pattern, indicating a first-order phase transition under certain conditions. This pattern is observed in both RPS and CFT, suggesting a consistent phase behavior across different frameworks. 2. **WGC in Different Phase Spaces**: - **EPST**: The condition for the WGC is \( H = \frac{\Omega^2}{M^2} - 1 > 0 \). - **RPST**: The condition is \( H = \frac{\Omega^2}{M^2} - G > 0 \). - **CFT**: The condition is \( H = \frac{\Omega^2}{M^2} - G > 0 \), with a more expansive parameter space for the WGC compared to EPST and RPST. 3. **WCCC at Critical Points**: The WCCC, which states that singularities should be concealed behind event horizons, is maintained at the critical juncture of black hole parameters. This is confirmed by the condition \( f(M_c, Q_c, r_c) = 0 \). 4. **Conclusion**: The WGC and WCCC are supported at the critical points of black holes, demonstrating their robustness within the critical ranges of black hole parameters. The study highlights the importance of considering the interplay between these conjectures in the context of charged black holes and dark matter.This paper explores the interplay between fundamental theoretical physics concepts, focusing on the consistency of the Weak Gravity Conjecture (WGC) and the Weak Cosmic Censorship Conjecture (WCCC) in the thermodynamics of charged black holes within the context of conformal field theory (CFT) and restricted phase space (RPS). The study specifically examines Reissner-Nordström (RN) black holes surrounded by perfect fluid dark matter (RN-PFDM). Key findings include: 1. **Thermodynamic Analysis**: The free energy of RN-AdS black holes in the presence of PFDM exhibits a distinctive swallowtail pattern, indicating a first-order phase transition under certain conditions. This pattern is observed in both RPS and CFT, suggesting a consistent phase behavior across different frameworks. 2. **WGC in Different Phase Spaces**: - **EPST**: The condition for the WGC is \( H = \frac{\Omega^2}{M^2} - 1 > 0 \). - **RPST**: The condition is \( H = \frac{\Omega^2}{M^2} - G > 0 \). - **CFT**: The condition is \( H = \frac{\Omega^2}{M^2} - G > 0 \), with a more expansive parameter space for the WGC compared to EPST and RPST. 3. **WCCC at Critical Points**: The WCCC, which states that singularities should be concealed behind event horizons, is maintained at the critical juncture of black hole parameters. This is confirmed by the condition \( f(M_c, Q_c, r_c) = 0 \). 4. **Conclusion**: The WGC and WCCC are supported at the critical points of black holes, demonstrating their robustness within the critical ranges of black hole parameters. The study highlights the importance of considering the interplay between these conjectures in the context of charged black holes and dark matter.