This study reports on the synthesis and characterization of novel perfluorinated organic polymers with azo- and azomethine-based linkers using nucleophilic aromatic substitution. The polymers were synthesized via the incorporation of decafluorobiphenyl and hexafluorobenzene linkers with diphenols in the basic medium. The variation in the linkers allowed the synthesis of polymers with different fluorine and nitrogen contents. The rich fluorine polymers were slightly soluble in THF and have shown molecular weights ranging from 4886 to 11,948 g/mol. All polymers exhibit thermal stability in the range of 350–500 °C, which can be attributed to their structural geometry, elemental contents, branching, and cross-linking. For instance, the cross-linked polymers with high nitrogen content, DAB-Z-1h and DAB-Z-1O, are more stable than azomethine-based polymers. The cross-linking was characterized by porosity measurements. The azo-based polymer exhibited the highest surface area of 770 m2/g with a pore volume of 0.35 cm3/g, while the open-chain azomethine-based polymer revealed the lowest surface area of 285 m2/g with a pore volume of 0.0872 cm3/g. Porous structures with varied hydrophobicities were investigated as adsorbents for separating water-benzene and water-phenol mixtures and selectively binding methane/carbon dioxide gases from the air. The most hydrophobic polymers containing the decafluorbiphenyl linker were suitable for benzene separation, while the best methane uptake values were 6.14 and 3.46 mg/g for DAB-Z-1O and DAB-A-1O, respectively. On the other hand, DAB-Z-1h, with the highest surface area and being rich in nitrogen sites, has recorded the highest CO2 uptake at 298 K (17.25 mg/g).