We explore the effect of growth conditions on the cation and anion chemistry, electrical leakage, conduction mechanisms, and ferroelectric and dielectric behavior of BiFeO3. Although it is possible to produce single-phase, coherently strained films in all cases, small variations in the pulsed-laser deposition growth process, specifically the laser repetition rate and target composition, result in films with chemistries ranging from 10% Bi-deficiency to 4% Bi-excess and films possessing Bi gradients as large a 6% across the film thickness. Corresponding variations and gradients in the O chemistry are also observed. As a result of the varying film chemistry, marked differences in surface and domain morphology are observed wherein Bi-deficiency stabilizes atomically smooth surfaces and ordered stripe domains. Subsequent investigation of the current-voltage response reveals large differences in leakage current density arising from changes in both the overall stoichiometry and gradients. In turn, the film stoichiometry drives variations in the dominant conduction mechanism including examples of Schottky, Poole-Frenkel, and modified Poole-Frenkel emission depending on the film chemistry. Finally, slightly Bi-excess films are found to exhibit the best low-frequency ferroelectric and dielectric response while increasing Bi-deficiency worsens the low-frequency ferroelectric performance and reduces the dielectric permittivity.