Facile synthesis of 2-10 nm-sized graphene quantum dots (GQDs) from graphite powder by organic solvent-assisted liquid exfoliation using a sonochemical method is reported in this study. Synthesized GQDs are well dispersed in organic solvents like ethyl acetoacetate (EAA), dimethyl formamide (DMF) and also in water. MALDI-TOF mass spectrometry reveals its selective mass fragmentation. Detailed characterizations by various techniques like X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), Raman spectroscopy and high resolution transmission electron microscopy (HRTEM) confirm the formation of disordered, functional GQDs. Density functional theory (DFT) calculation confirms HOMO-LUMO energy gap variation with changing size and functionalities. Photoluminescence (PL) properties of as-prepared GQDs were studied in detail. The ensemble studies of GQDs showed excellent photoluminescence properties comprising normal and upconverted fluorescence, delayed fluorescence and room-temperature phosphorescence. PL decay dynamics of GQDs has been explored using time-correlated single-photon technique (TCSPC) as well as femtosecond fluorescence upconversion technique. In vitro cytotoxicity study reveals its biocompatibility and high cell viability (>91%) even at high concentration (400 μg mL-1) of GQDs in Chinese Hamster Ovary (CHO) cells.