Waste oils are becoming increasingly more important as feedstock for the production of fuels and glycerol as byproduc. Optimization of homogeneous transesterification of waste frying oil (WFO) to biodiesel over hydroxide potassium (KOH) catalyst have been investigated. In this respect, response surface methodology (RSM) was applied to determine the relationships between methanol and WFO molar ratio (3:1–12:1), KOH concentration (0.5%–2%) and temperature (25–65 °C) on the conversion yield. Transesterification of WFO produced 96.33% maximum methyl ester yield at the optimum methanol/WFO molar ratio 7.3:1, KOH loading 0.5 wt. % and the reaction temperature was 58.30 °C. The physicochemical properties of optimized biodiesel met the requirements of the European Norm 14214, such as kinematic viscosity at 40 °C 4.57 mm/s2, the sulfur content 0.005 wt. %, and the density at 15 °C 889.3 kg/m3. This study also examined the accelerated oxidation of biodiesel and biodiesel/diesel blends under combined temperature and air effect at different periods of time while measuring their acidity. Results have shown that total acid number increased proportionally to the biodiesel content of the biodiesel/diesel blends from 0.5 mgKOH/g for B7 (7% (v/v) biodiesel and 93% (v/v) diesel) up to 2.8 mg KOH/g for B100 (100% biodiesel). The synthesized trans-esterified oil can be a potential alternative to petrodiesel, hence its application at an industrial scale. This work also reports some properties of crude glycerol (CG) derived from biodiesel from WFO. The glycerol yield (%), pH, water content (wt. %), density at 15 °C (g/cm3), and kinematic viscosity at 40 °C (mm2/s) was analyzed according to standard test methods.